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Brucellosis, as a prevalent zoonosis caused by Brucella, primarily spreads in northern pastoral regions of China. The high levels of perceived risk about brucellosis before 2009 were largely suspected in Jilin province, as well as its effect in stemming the transmission of brucellosis. We will devise two epidemic models to investigate the effects of spontaneous changes in herder’s behavior awareness on the transmission of brucellosis. The global dynamics of these models will be thoroughly analyzed. The models are utilized to fit the data of newly infected cases of brucellosis in Jilin province from 2002–2020. The vital information-induced parameters of brucellosis have been estimated by the Markov Chain Monte Carlo (MCMC) method. The basic reproduction numbers are calculated as R0 = 1.767 prior to 2009 and R0 = 0.921 after 2009. Moreover, our findings indicate that a one-year delay in the implementation of pilot work in Jilin province by the government would result in a 50% increase in the peak number of newly infected brucellosis cases, surpassing 5000. On the contrary, if the government were to implement the pilot work in Jilin province one year ahead of schedule, there would be a 40% reduction in the peak number of newly infected brucellosis cases. Furthermore, the results suggest that enhancing the voluntary detection and protection rate is more effective than increasing voluntary rates. Information-induced detection and protection play a crucial role in curbing the spread of brucellosis. The increase in the reactivity factor of voluntary detection C from 0.00128 to 0.0128 will result in a reduction of the incidence rate of human brucellosis cases to less than 1 per 100,000, enabling the achievement of the national control target seven years ahead of schedule. The insights shed herein may be conductive to suppress the spread of brucellosis in other areas. [ABSTRACT FROM AUTHOR]

In this article, a cytokine-enhanced viral infection model with cytotoxic T lymphocytes (CTLs) immune response and antibody immune response is proposed and analyzed. The model contains six compartments: uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, viruses, CTLs and antibodies. Different from the previous works, this model not only considers virus-to-cell transmission and cell-to-cell transmission, but also includes a new infection mode, namely cytokine-enhanced viral infection. The incidence rates of the healthy CD4+T cells with viruses, infected cells and inflammatory cytokines are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. Firstly, we prove that all the solutions of the model are nonnegative and uniformly bounded. Then, five key parameters with strong biological significance, namely the virus basic reproduction number R0, CTLs immune response reproduction number R1, antibody immune response reproductive number R2, CTLs immune competitive reproductive number R3 and antibody immune competitive reproductive number R4 are derived. Then, by using Lyapunov's method and LaSalle's invariance principle, we have shown the global stability of each equilibrium. In addition, the numerical simulation results also show that the theoretical results are correct. Finally, we formulate an optimal control problem and solve it using Pontryagins Maximum Principle and an efficient iterative numerical methods. The results of our numerical simulation show that it is very important to control the infection between viruses and cells and between cells and inflammatory cytokines for controlling HIV. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an age‐structured epidemiological compartment model and its respective problem, applied but not limited to the COVID‐19 pandemic, in order to investigate the role of the age of the individuals in the evolution of epidemiological phenomena. We investigate the well‐posedness of the model, as well as the global dynamics of it in the sense of basic reproduction number, via constructing Lyapunov functions. [ABSTRACT FROM AUTHOR]

Researchers and transnational public health organizations have recognized aerosol transmission as an essential route of COVID‐19 transmission. Therefore, improving ventilation systems is now adopted as a core preventive measure. As young children aged 2–6 in kindergartens generally lack vaccine protection and multiple infection clusters have been identified during the pandemic, we aimed to quantify the risk of aerosol transmission in kindergartens in Taipei, Taiwan. From August to November 2021, we conducted on‐site visits and continuously monitored indoor air quality indicators including carbon dioxide (CO2) in a kindergarten located in northern Taiwan. We utilized the Wells–Riley model to estimate the basic reproduction number (R0) of each classroom and staff office, with input parameters including the number of occupants, duration of their stay, and indoor/outdoor CO2 concentration. Contagious settings were defined as those where the R0 estimate exceeded 1. We conducted a scenario/sensitivity analysis to assess the effect of simulated improvement measures. During school hours, the average concentration of CO2 in each classroom and the staff office was often more than 400 ppm higher than the outdoor levels. The R0 estimates gradually increased from Monday to Friday and throughout school hours, corresponding to the hourly and daily distribution of the CO2 concentration, which could not dissipate completely during off‐duty time. The R0 estimates during school hours ranged from 3.01 to 3.12 in classrooms with a maximum of 30 occupants. To lower the R0 estimate, it is imperative to substantially reduce the number of occupants, the duration of their stay, and indoor CO2 concentration. The risk of outbreaks of cluster infections in kindergartens should not be underestimated. Feasible strategies to mitigate this risk should include improving ventilation systems through engineering control and limiting the number of indoor occupants and their time staying indoor through administrative control. [ABSTRACT FROM AUTHOR]

Temperature and water availability significantly influence mosquito population dynamics. We have developed a method, integrating experimental data with insights from mosquito and thermal biology, to calculate the basic reproduction number (RM) for urban mosquito species Aedes albopictus and Aedes aegypti. RM represents the number of female mosquitoes produced by one female during her lifespan, indicating suitability for growth. Environmental conditions, including temperature, rainfall and human density, influence RM by altering key mosquito life cycle traits. Validation using data from Spain and Europe confirms the approach's reliability. Our analysis suggests that temperature increases may not uniformly benefit Ae. albopictus proliferation but could boost Ae. aegypti expansion. We suggest using vector RM maps, leveraging climate and environmental data, to predict areas susceptible to invasive mosquito population growth. These maps aid resource allocation for intervention strategies, supporting effective vector surveillance and management efforts. [ABSTRACT FROM AUTHOR]

Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis of the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene, and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies demonstrated that strategy 2, 7, and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs. [ABSTRACT FROM AUTHOR]

In this paper, we propose an epidemic model with the impact of information intervention and general incidence rate in deterministic and stochastic environment, respectively. The information intervention prompts susceptible individuals to change their behavior to protect themselves from infection. First, the asymptotic dynamics of the disease-free equilibrium and the unique endemic equilibrium are analyzed and the results indicate that the basic reproduction number is a pointy disease threshold about the stability under some conditions. Then, we formulate the corresponding stochastic model by perturbing the disease transmission rate and information response rate parameters by white noise terms and provide verifiable sufficient conditions for extinction and persistence in mean. Two sufficient conditions for extinction show that if the noise intensity of the disease transmission rate is large enough or small enough, the infected population of the stochastic system will tend to go extinct. For the persistence, we get the sufficient conditions which guarantee the infected population to be persistent in the mean. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic and the stochastic system. [ABSTRACT FROM AUTHOR]

We propose, in this paper, a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment, which is coupled with some reaction–diffusion equations and first-order partial differential equations. The precise formulation of basic reproduction number ( ℛ 0 ) is deduced, which characterizes the elimination or prevalence of this disease. Specifically, the disease-free steady state is globally asymptotically stable for ℛ 0 ≤ 1 but unstable for ℛ 0 > 1. Further, the phage invasion reproduction number ℛ 1 is also obtained, which portrays the impact of phages on Vibrio cholerae in the environment. That is, for ℛ 0 > 1 , the phage-free endemic steady state is globally asymptotically stable if ℛ 1 ≤ 1 , and the phage-present endemic steady state is globally asymptotically stable if ℛ 1 > 1. Numerical simulations are introduced for the purpose of verifying the main results. [ABSTRACT FROM AUTHOR]

Changes in host species richness can alter infection risk and disease levels in multi‐host communities. I review theoretical predictions for direct and environmental transmission pathogens about the effects of host additions (or removals) on three commonly used disease metrics: the pathogen community reproduction number R0 and infection prevalence and infected density in a focal host. To extend this prior work and explain why predictions differ between metrics, I analyze Susceptible Infected‐Recovered‐type models of an environmentally transmitted pathogen and multiple host species that compete for resources. Using local sensitivity analysis, I show how trait‐mediated and density‐mediated indirect effects drive each metric's response to variation in an added host's ability to transmit a pathogen, the added host's density, and the pathogen transmission mechanism. For each disease metric, the responses are typically predicted by the added host's ability to transmit the pathogen when interspecific competition is weak whereas the responses can be altered by shifts in host densities when interspecific competition is strong. In addition, the three metrics often respond in the same direction. However, the metrics can respond in different directions for three reasons: (1) differences between the ability of exposed individuals to transmit the pathogen over the length of time the individuals are infected (i.e., host competence) and a host population's instantaneous net rate of production of infectious propagules; (2) strong density‐mediated feedbacks driven by disease‐induced mortality; and (3) host additions or removals cause large changes in focal host density via competition or disease‐induced mortality. This study extends and unifies prior theoretical studies, and helps identify the rules governing the context‐dependent relationships between host species richness and the three metrics of disease. [ABSTRACT FROM AUTHOR]

This paper is concerned with spatiotemporal dynamics of a fractional diffusive susceptible-infected-susceptible (SIS) epidemic model with mass action infection mechanism. Concretely, we first focus on the existence and stability of the disease-free and endemic equilibria. Then, we give the asymptotic profiles of the endemic equilibrium on small and large diffusion rates, which can reveal the impact of dispersal rates and fractional powers simultaneously. It is worth noting that we have some counter-intuitive findings: controlling the flow of infected individuals will not eradicate the disease, but restricting the movement of susceptible individuals will make the disease disappear. [ABSTRACT FROM AUTHOR]

The multi drug-resistant Neisseria gonorrhoeae has been classified by the World Health Organisation (WHO) as a high-priority global public health problem. This underlines the need for better understanding of the transmission dynamics and proposing an optimal intervention strategy to control the disease. In this article, a deterministic mathematical model for the transmission dynamics of gonorrhoea as an antibiotic resistant disease in a population with an imperfect vaccination is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection interventions to reduce antibiotic resistant cases. The threshold parameter R 0 , the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibits a backward bifurcation for R 0 < 1. However, if the efficacy of the vaccine is 100% without a waning effect, the model is shown to be without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R 0 < 1. The global sensitivity analysis of the model to variations in parameter values is also performed to determine the most influential parameters on the disease transmission. Moreover, the optimal control analysis of the full model is presented and the optimal intervention strategies are proposed. The proposed intervention strategies are shown to be able to control the disease within a relatively shorter period of time. Finally, numerical experiments are presented to support the theoretical analysis of the model. • Imperfect vaccination is not helpful to eradicate the disease from the population. • Awareness campaign about the antibiotic resistant strain can reduce the transmission of the disease. • Sensitive parameters for the transmission dynamics of the disease are identified. • With the use of the optimal control analysis, cost effective intervention measures are proposed. [ABSTRACT FROM AUTHOR]

Considering the factors such as time delay in the propagation of rumors and the inability to spread rumors due to the forced silence of network regulators, in this study, based on the SIR model, combined with the rumorrefuging mechanism and the space theory, nodes in the network were divided into susceptible node S, infective node I, rumor-refuging node C and recovered node R, a new SICR rumor propagation model was proposed. Firstly, the dynamic equation of rumor propagation in homogeneous network structure was given by means of average field theory, the existence of equilibrium point was analyzed, and the basic reproduction number of the model was calculated by using the next generation matrix method. It was found that the basic reproduction number was related to the propagation rate, average degree, migration rate, migration rate, forced silence rate, and recovery rate of infective nodes. Secondly, the local asymptotic stability of the equilibrium point was analyzed by Routh-Hurwitz criterion, and the global asymptotic stability was analyzed by LaSalle's invariance principle. Finally, the correctness of the theoretical results was verified by numerical simulation experiments. The simulation results showed that SICR model considering the rumor-refuting mechanism could suppress the rumor propagation better than SIR model. Based on Dataset&lowbar;R6 dataset, the parameters of the model were fitted by least square method, and the R2 of the model was 0. 950 8. [ABSTRACT FROM AUTHOR]

To study the impact of stochastic environmental variations on the transmission dynamics of HTLV-I infection, a stochastic HTLV-I infection model with a nonlinear CTL immune response is developed. By selecting an appropriate stochastic Lyapunov functional, we discussed the qualitative behavior of the stochastic HTLV-I infection model, such as existence and uniqueness, stochastically ultimate bounded, and uniformly continuous. We find adequate criteria for the presence of a distinct ergodic stationary distribution of the HTLV-I system when the stochastic basic reproduction number is bigger than one by a careful mathematical examination of the HTLV-I infection model. Furthermore, when the stochastic fundamental reproduction number (R 0 E) is smaller than one, we provide sufficient circumstances for the extinction of the diseases. To illustrate our analytical conclusions, we ran numerical simulations. We also plotted the time series evolution of the CTL immune response, healthy CD4+T cells, latently infected CD4+T cells, and actively infected CD4+T cells in relation to the white noise. In the numerical simulation, we investigate that small intensities of a single white noise can sustain a very slight fluctuation in each population. The high intensities of only one white noise can maintain the irregular recurrence of each population. Both the deterministic and stochastic models have the same solution if the random noises are too small. [ABSTRACT FROM AUTHOR]

In order to reveal the transmission dynamics of Avian influenza and explore effective control measures, we develop a non-local delayed reaction-diffusion model of Avian influenza with vaccination and multiple transmission routes in the heterogeneous spatial environment, taking into account the incubation period of Avian influenza in humans and poultry. Firstly, the well-posedness of model is obtained which includes the existence, uniform boundedness and the existence of global attractor. Further, the basic reproduction number R 0 of this model is calculated by the definition of the spectral radius of the next generation operator, and its variational form is also derived. Further, the global dynamics of the model is established based on the biological significance of R 0 . To be more precise, if R 0 < 1 , the disease-free steady state is globally asymptotically stable (i.e., the disease is extinct), while if R 0 > 1 , the disease is uniformly persistent and model admits at least one endemic steady state. In addition, by constructing suitable Lyapunov functionals, we achieve the global asymptotic stability of the disease-free and endemic steady states of this model in spatially homogeneous. Finally, some numerical simulations illustrate the main theoretical results, and discuss the sensitivity of R 0 on the model parameters and the influences of non-local delayed and diffusion rates on the transmission of Avian influenza. The theoretical results and numerical simulations show that prolonging the incubation period, controlling the movement of infected poultry, and regular disinfecting the environment are all effective ways to prevent Avian influenza outbreaks. [ABSTRACT FROM AUTHOR]

A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system's existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) 0 is locally asymptotically stable (LAS) when ℛ v < 1. Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) ∗ for ℛ v > 1 and 0 for ℛ v ≤ 1. The existence of bifurcation analysis in the model is investigated, and it is shown the system possesses the forward bifurcation phenomenon. Sensitivity analysis has been performed to determine the sensitive parameters that impact ℛ v. We consider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model. The computed basic reproduction number obtained using the real cases is ℛ 0 ≈ 3.6615. Various numerical results regarding disease elimination of the sensitive parameters are shown graphically. [ABSTRACT FROM AUTHOR]

Marburg virus, like Ebola, causes haemorrhagic disease with high fatality rates. We developed a deterministic SEIRDVT model incorporating vaccination and treatment to study the disease dynamics. Qualitative analysis revealed a backward bifurcation when R 0 = 1 , meaning R 0 < 1 is insufficient to eradicate the virus. Sensitivity analysis using Latin Hypercube Sampling showed that applying four control measures—screening, prevention, continuous vaccination, and treatment—significantly reduced transmission. The most cost-effective strategy combines prevention, vaccination, and treatment. These findings provide a framework for designing efficient interventions to combat Marburg virus. [ABSTRACT FROM AUTHOR]

In this research, the ongoing COVID-19 disease by considering the vaccination strategies into mathematical models is discussed. A modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including susceptible (Sα), exposed (Eα), infected (Uα), quarantined (Qα), vaccinated (Vα), and recovered (Rα) individuals. Using conformable derivatives, a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. The basic reproduction number (R0), which is an essential indicator of disease transmission, is the subject of investigation calculating using the next-generation matrix approach. We also compute the R0 sensitivity indices, which offer important information about the relative influence of various factors on the overall dynamics. Local stability and global stability of R0 have been proved at a disease-free equilibrium point. By designing the finite difference approach of the conformable fractional derivative using the Taylor series. The present methodology provides us highly accurate convergence of the obtained solution. Present research fills research addresses the understanding gap between conceptual frameworks and real-world implementations, demonstrating the vaccination therapy's significant possibilities in the struggle against the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of invasion dynamics of Aedes aegypti mosquitoes via a reaction-diffusion-advection system in closed advective environments with spatial heterogeneity. We first establish the threshold dynamics of the system in terms of the basic reproduction number R 0. Then, based on the analysis of some properties of R 0 with respect to the diffusion rate D and the advection rate q , we provide a complete classification for the dynamics of the system in the D − q plane. The findings reveal that spatial heterogeneity, diffusion rate, advection rate and maturity rate all have substantial influences on mosquito invasion dynamics, which is much more complicated than the results in the homogeneous case. [ABSTRACT FROM AUTHOR]

This paper is concerned with the qualitative analysis of a diffusion SIR epidemic model with networked delay and nonlinear incidence rate. First, we prove the existence and uniqueness of the model by using the method of upper and lower solutions. Then, we prove that the trivial equilibrium (0, 0) is unstable; the disease‐free equilibrium (N, 0) is locally asymptotically stable if the reproduction number R0≤1 and unstable if R0>1; the endemic equilibrium (S∗, I∗) is locally asymptotically stable if R0≤R1 or if R1τ10∗. Moreover, when R1

During peak passenger flow periods, congestion propagation directly affects the operational safety and efficiency of multi-mode rail transit interconnections. By analyzing the key factors affecting congestion propagation, such as the train stop schedule, and considering parameters such as the basic reproduction number and propagation threshold, this study proposes a multi-mode rail transit susceptible-infected-recovered-susceptible (MRT-SIRS) epidemic model to analyze passenger flow congestion propagation. Simulation experiments and sensitivity analyses using data from the multi-mode rail transit in Beijing, China, were conducted to examine the influence mechanism of key factors on congestion propagation. The degree of influence of each factor was investigated using Gray correlation analysis. Each key factor, including the propagation and recovery rates, influences congestion propagation differently. The results of this study may provide theoretical support for the efficient operation and management of multi-mode rail transit systems. [ABSTRACT FROM AUTHOR]

Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models. [ABSTRACT FROM AUTHOR]

This research article investigates the dynamics of alcohol consumption and the impact of addiction treatment using the continuous mathematical model SaEaDaTaRa. The study is significant as it incorporates the Atangana–Baleanu Caputo fractional derivatives, offering a novel approach to establishing the existence and uniqueness of solutions within this context. Our model formulation captures various stages of alcohol consumption and treatment, providing a comprehensive framework for analysis.We employ the next-generation matrix approach to explore the disease-free and endemic equilibria to calculate the basic reproduction number, R0. Sensitivity analysis is conducted to identify the parameters that most significantly influence R0, which helps in understanding the dynamics of alcohol use and the effectiveness of intervention strategies. The local and global stability of both the alcohol-free and alcohol-present equilibria are rigorously examined to provide insights into potential long-term outcomes of alcohol consumption in the presence of treatment facilities.Furthermore, we utilize Lagrange interpolation polynomial in a numerical framework implemented in Python to perform detailed simulations and validate our theoretical results. This numerical analysis helps visualize the model's predictions and understand the temporal evolution of alcohol consumption within the population. [ABSTRACT FROM AUTHOR]

This study delves into the often‐overlooked impact of immature mosquitoes on the dynamics of malaria transmission. By employing a mathematical model, we explore how these aquatic stages of the vector shape the spread of the disease. Our analytical findings are corroborated through numerical simulations conducted using the Runge–Kutta fourth‐order method in MATLAB. Our research highlights a critical factor in malaria epidemiology: the basic reproduction number R0. We demonstrate that when R0 is below unity R0<1, the disease‐free equilibrium exhibits local asymptotic stability. Conversely, when R0 surpasses unity R0>1, the disease‐free equilibrium becomes unstable, potentially resulting in sustained malaria transmission. Furthermore, our analysis covers equilibrium points, stability assessments, bifurcation phenomena, and sensitivity analyses. These insights shed light on essential aspects of malaria control strategies, offering valuable guidance for effective intervention measures. [ABSTRACT FROM AUTHOR]

The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model's solutions, calculating the basic reproduction number ( R 0 ) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin's maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin‐users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence using a mathematical model with distributed delay. First, we show the existence threshold parameter R0$$ {\mathfrak{R}}_0 $$, which we call the basic reproduction number of the spread of heroin use. We prove, via the Lyapunov direct method, that the drug‐free equilibrium is globally asymptotically stable if R0<1$$ {\mathfrak{R}}_0<1 $$. If R0>1$$ {\mathfrak{R}}_0>1 $$, the drug dependence persists, and the drug equilibrium is globally asymptotically stable. We give three possible scenarios to find the optimal awareness program strategy that puts the heroin epidemic under control. These scenarios take into consideration the reachability of the population, the immunity against heroin addiction, and the effectiveness of the program to contain the use of heroin in the population and bring R0$$ {\mathfrak{R}}_0 $$ below one. [ABSTRACT FROM AUTHOR]

Leptospirosis is an emerging zoonotic disease with high health and economic damage. In this study, we developed a deterministic mathematical model that describes the dynamics of leptospirosis transmission within a cattle herd, incorporating asymptomatic infected and vaccinated compartments. The study examined the transmission role of asymptomatic cattle that contaminate herds without farmers' knowledge. We proved the well-posedness of the proposed model and found the basic reproduction number using the next-generation matrix. Analytically, we demonstrated that the disease-free equilibrium point is locally and globally asymptotically stable when R 0 is less than unity and is otherwise unstable. Graphically, we further established the local asymptotic stability of disease-free and endemic equilibria. Sensitivity analysis showed that the contact rate with asymptomatic infected cattle, β A , is the most sensitive parameter in the stated model, followed by the recovery rate of asymptomatic infected cattle, σ , and the vaccination rate of susceptible cattle, τ . Numerical simulations revealed that a reduction in contact rate with asymptomatic infected cattle significantly reduced pathogen Leptospira transmission in the herd. In addition, fostering the recovery rate of asymptomatic infected cattle can significantly reduce new infections in the herd. Furthermore, augmenting the vaccination rate among susceptible cattle resulted in a notable decrease in disease prevalence within the herd. Findings of this study underscore the remarkable importance of targeted interventions, such as reducing contact rates with asymptomatic infected cattle, increasing recovery rates using proper treatments, and enhancing vaccination efforts to manage leptospirosis transmission in cattle herds. [ABSTRACT FROM AUTHOR]

Non-pharmaceutical interventions (NPIs) are effective in mitigating infections during the early stages of an infectious disease outbreak. However, these measures incur significant economic and livelihood costs. To address this, we developed an optimal control framework aimed at identifying strategies that minimize such costs while ensuring full control of a cross-regional outbreak of emerging infectious diseases. Our approach uses a spatial SEIR model with interventions for the epidemic process, and incorporates population flow in a gravity model dependent on gross domestic product (GDP) and geographical distance. We applied this framework to identify an optimal control strategy for the COVID-19 outbreak caused by the Delta variant in Xi'an City, Shaanxi, China, between December 2021 and January 2022. The model was parameterized by fitting it to daily case data from each district of Xi'an City. Our findings indicate that an increase in the basic reproduction number, the latent period or the infectious period leads to a prolonged outbreak and a larger final size. This indicates that diseases with greater transmissibility are more challenging and costly to control, and so it is important for governments to quickly identify cases and implement control strategies. Indeed, the optimal control strategy we identified suggests that more costly control measures should be implemented as soon as they are deemed necessary. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. More populated and economically developed regions require a robust regular surveillance mechanism to ensure timely detection and control of imported infections. Regions with higher GDP tend to experience larger-scale epidemics and, consequently, require higher control costs. Notably, our proposed optimal strategy significantly reduced costs compared to the actual expenditures for the Xi'an outbreak. Author summary: In the early stage of the outbreak of an emerging infectious disease, non-pharmaceutical interventions (NPIs) are the most effective way to control the spread of the disease given unavailability of effective medicines or vaccines. However, the implementation of NPIs may have a certain negative impact on the society and economy. There are many challenges to designing an effective and economical control regime on the basis of spatial, populate and economical heterogeneity. We developed a modelling framework to couple transmission dynamics, all possible control measures and the spatial mobility, aiming at controlling the outbreak spreading across regions and reducing the economic losses caused by control measures. We applied this framework to identify the optimal control strategy for the COVID-19 outbreak in Xi'an City, China, between December 2021 and January 2022. We analyzed the key factors related to the outbreak size and control cost, and the results showed that the outbreak size and control cost were significantly correlated with the transmissibility of the virus and the demographic and economic conditions of the epidemic area. Our results demonstrate that optimal control regimes exhibit spatial, economic, and population heterogeneity. [ABSTRACT FROM AUTHOR]

In an ecosystem, harvesting infected prey can assist in managing and containing the spread of the illness within the prey species. On the other hand, the harvesting of predators can be beneficial as it regulates their numbers, preventing them from over-consuming prey and subsequently preserving existence of the prey population. This study introduces a predator–prey model that encompasses prey infection, predator–prey interactions influenced by fear, switching and harvesting. We derive an analytic expression for the basic reproduction number, a critical determinant of disease spread. We investigate the global stability of disease-free and endemic equilibria contingent on the basic reproduction number’s value, highlighting the potential for disease eradication by maintaining it below unity. In-depth analysis of the deterministic model is undertaken, with a focus on Hopf bifurcations that delineate thresholds for disease-free and endemic states. Furthermore, the deterministic model is extended to incorporate environmental stochasticity. We obtain the conditions under which population extinction occurs. Our findings elucidate how the intensity of environmental noise influences population dynamics, providing valuable insights into extinction risks under varying noise levels. [ABSTRACT FROM AUTHOR]

In this work, a two‐sex deterministic model for human papillomavirus (HPV) is developed to assess the impact of screening awareness and vaccination on the transmission dynamics. We provide a detailed analysis of the HPV model and established results for boundedness of the solutions and existence of a positively invariant and attracting set. The basic reproduction number R0$$ {R}_0 $$ is characterized, and it is shown that the disease‐free equilibrium is locally asymptotically stable if R0<1$$ {R}_0<1 $$ and the system is uniformly persistent if R0>1$$ {R}_0>1 $$. Sensitivity analysis of R0$$ {R}_0 $$ reveals that HPV vaccination can mitigate HPV transmission, and HPV vaccination along with screening can further reduce the spread of HPV infection. Numerical simulations showed that the public awareness of screening after being vaccinated is contributing to reduce the spread of epidemic, and the role of screening awareness in controlling the disease was significantly greater among men than women. Besides, the numerical simulations reveal that increasing vaccination rates for male is effective in controlling HPV transmission. Hence, it is necessary to enhance the screening for men. Moreover, increasing vaccination rates is more effective than increasing screening awareness in eliminating the epidemic. [ABSTRACT FROM AUTHOR]

In this work, we mechanistically formulate a generalized cholera model with nonlocal time delay to study the impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment. Mathematical challenges lie in the fact that (i) the generalized cholera model considers the intrinsic growth of short-lived hyperinfectious (HI vibrios) state of V. cholerae and lower-infectious (LI vibrios) state of V. cholerae simultaneously; and (ii) this article originally derives the detailed classifications of spatial dynamics for the cholera model with some generally functional response functions, non-uniformness of diffusion rates and nonlocal time delay. We introduce three basic reproduction numbers: one is for HI state of V. cholerae , the other is for LI state of V. cholerae , and another is for the cholera disease in the host population. Based on these basic reproduction numbers, we further establish the global threshold dynamics. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of infectious hosts. [ABSTRACT FROM AUTHOR]

In this paper, a two-group SIR reaction-diffusion epidemic model with nonlocal dispersal and spatial-temporal delay based on within-group and inter-group transmission mechanisms is investigated. The basic reproduction number R 0 is calculated using the method of next-generation matrix. The critical wave speed c m * is determined by analyzing the distribution of roots of the characteristic equation. When R 0 > 1 and wave speed c ⩾ c m * , the existence of traveling waves connecting disease-free and endemic steady states is obtained by constructing sub- and super-solutions and a Lyapunov functional, and applying Schauder's fixed-point theorem and a limit argument. When R 0 > 1 and 0 < c < c m * , the nonexistence of traveling waves connecting disease-free and endemic steady states is proven by contradiction and two-sided Laplace transform. This indicates that the critical wave speed c m * is exactly the minimum wave speed. Numerical simulations are carried out to illustrate theoretical results. The dependence of the minimal speed c m * on time delay, diffusion rates and contact rates is discussed, showing that the longer the latent period and the lower the diffusion rates of infected individuals and the inter-group transmission rates between groups, the slower the spread of disease. [ABSTRACT FROM AUTHOR]

Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility ( S 1 ), individuals with high susceptibility ( S 2 ), infected individuals (I), exposed individuals (E), and recovered individuals (R). To capture the complex dynamics of EVD, we employ a Φ -piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the Φ -Caputo derivative in the first interval and the Φ -ABC derivative in the second interval. The study determines the basic reproduction number R 0 , analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system's behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD. [ABSTRACT FROM AUTHOR]

The spread of epidemic diseases is often considered to be bound up with human behavior. Both treatment and awareness-raising are seen as important preventive measures during an outbreak. In this paper, an SEIR model on heterogeneous network containing saturated treatment function with media information variable is constructed. Through mathematical analysis, the basic reproduction number and equilibriums of the system are derived. The global stability of disease-free equilibrium is further proved based on LaSalle's invariant principle. It is also found that with a gradual increase of the delayed treatment parameter, the system exhibits a transition from forward bifurcation to backward bifurcation with the variation of the basic reproduction number. Finally, an optimal control problem is formulated with both treatment rate and media information dissemination rate as control variables and solved using the Pontryagin's maximum principle. All the above results are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system's solutions, the research ensures the model's well-posedness, guaranteeing its mathematical soundness and practical relevance. The study calculates and evaluates the equilibrium points and the basic reproduction numbers R 0 1 and R 0 2 to understand the dynamic behavior of the model under different parameter settings. Through the application of the Lyapunov method, the research examines the asymptotic global stability of the system, determining whether it will converge to a particular equilibrium state over time. Furthermore, Hopf bifurcation theory is employed to investigate potential periodic solutions and bifurcation scenarios, highlighting how the system might shift from stability to periodic oscillations under certain conditions. By utilizing the Adams-Bashforth-Moulton numerical simulation method, the theoretical results are validated, reinforcing the conclusions and demonstrating the model's applicability in real-world contexts. It emphasizes the importance of fractional-order models in addressing epidemiological issues related to time delays (τ), individual heterogeneity (m, k), and memory effects (θ), offering greater accuracy compared with traditional integer-order models. In summary, this research provides a theoretical foundation and practical insights, enhancing the understanding and management of epidemic dynamics through fractional-order epidemic models. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has underscored the necessity of implementing non-pharmaceutical interventions such as lockdowns to mitigate the spread of infectious diseases. This study aims to model the impact of lockdown measures on the progression of an epidemic. Using a combination of compartmental models, specifically a novel delay model, we analyze the effects of varying lockdown intensities and durations on disease transmission dynamics. The results highlight that timely and stringent lockdowns can significantly reduce the peak number of infections and delay the epidemic's peak, thereby alleviating pressure on healthcare systems. Moreover, our models demonstrate the importance of appropriate lifting of lockdowns to prevent a resurgence of cases. Analytical and numerical results reveal critical thresholds for lockdown efficacy from the epidemiological point of view, which depend on such factors as the basic reproduction number ( ℜ 0 ), disease duration, and immunity waning. In the case of a single outbreak with permanent immunity, we analytically determine the optimal proportion of isolated people which minimizes the total number of infected. While in the case of temporary immunity, numerical simulations show that the infectious cases decrease with respect to the proportion of isolated people during lockdowns; as we increase the proportion of isolated people, we have to increase the duration of lockdowns to obtain periodic outbreaks. Further, we assess the influence of epidemic with or without lockdown on the economy and evaluate its economical efficacy by means of the level of population wealth. The percentage of productive individuals among isolated people influences the wealth state of the population during lockdowns. The latter increases with the rise of the former for fixed epidemic parameters. This research provides valuable insights for policymakers in designing effective lockdown strategies to control future epidemics. [ABSTRACT FROM AUTHOR]

In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as R 1 and R 2 . The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when R 1 and R 2 are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin's maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a reaction–diffusion vector–host disease model with advection effect in an one‐dimensional domain. We introduce the basic reproduction number (BRN) ℜ0$\Re _0$ and establish the threshold dynamics of the model in terms of ℜ0$\Re _0$. When there are no advection terms, we revisit the asymptotic behavior of ℜ0$\Re _0$ w.r.t. diffusion rate and the monotonicity of ℜ0$\Re _0$ under certain conditions. Furthermore, we obtain the asymptotic behavior of ℜ0$\Re _0$ under the influence of advection effects. Our results indicate that when the advection rate is large enough relative to the diffusion rate, ℜ0$\Re _0$ tends to be the value of local basic reproduction number (LBRN) at the downstream end, which enriches the asymptotic behavior results of the BRN in nonadvection heterogeneous environments. In addition, we explore the level set classification of ℜ0$\Re _0$, that is, there exists a unique critical surface indicating that the disease‐free equilibrium is globally asymptotically stable on one side of the surface, while it is unstable on the other side. Our results also reveal that the aggregation phenomenon will occur, namely, when the ratio of advection rate to diffusion rate is large enough, infected individuals will gather at the downstream end. [ABSTRACT FROM AUTHOR]

Mathematical analysis of epidemics is crucial for long‐term disease prediction and helps to guide decision‐makers in terms of public health policy. In this study, we develop a within‐host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well‐posedness and biological feasibility of the model in terms of proving the non‐negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite‐free equilibrium is locally and globally stable if the basic reproduction number, R0<1, otherwise, if R0>1, then there exist four parasite‐persistence equilibria. The stability conditions of these parasite‐persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host's body. [ABSTRACT FROM AUTHOR]

The spatial structure of a host population has a profound effect on the dynamics of infectious diseases. The basic reproduction number, a central quantity in the study of epidemic dynamics, is affected by host clustering as well as host density. Several authors have developed methods to quantify the basic reproduction number in a spatially structured host population. The methods used and the expressions derived are however difficult to apply to real life spatial host structures. In this paper we introduce an explicit expression for the basic reproduction number using the O‐ring statistic, developed in spatial statistics, that quantifies the host density as a function of the distance from a randomly selected host individual. The O‐ring statistic is frequently used in the study of the ecology of spatially structured plant populations, being a convenient summary of the properties of a landscape by way of a single function. The connection we develop between spatial statistics and epidemic dynamics can be used to study the effect of host spatial pattern on the basic reproduction number of infectious diseases. As well as showing how explicit expressions for the basic reproduction number can be derived for landscapes with standard structures, our expression for the basic reproduction number is tested against a simulation model. The model structure in our simulation is motivated by the spread of a plant disease epidemic, although it is applicable more broadly. The agreement between our analytic expression for the basic reproduction number and the corresponding numeric quantity extracted from simulations is close to perfect across a wide range of landscape structures and model parameterisations, and including cases in which more than one species of host is at risk of infection. [ABSTRACT FROM AUTHOR]

Hand, foot and mouth disease (HFMD) is a Class C infectious disease that carries particularly high risk for preschool children and is a leading cause of childhood death in some countries. We mimic the periodic outbreak of HFMD over a 2-year period—with differing amplitudes—and propose a dynamic HFMD model that differentiates transmission between mature and immature individuals and uses two possible optimal-control strategies to minimize case numbers, total costs and deaths. We parameterized the model by fitting it to HFMD data in mainland China from January 2011 to December 2018, and the basic reproduction number was estimated as 0.9599. Sensitivity analysis demonstrates that transmission between immature and mature individuals contributes substantially to new infections. Increasing the isolation rates of infectious individuals—particularly mature infectious individuals—could greatly reduce the outbreak risk and potentially eradicate the disease in a relatively short time period. It follows that we have a reasonable chance of controlling HFMD if we can reduce transmission in children under 7 and isolate older infectious individuals. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and analyze a compartmental model of visceral leishmaniasis (VL). We validate our model by calibrating it to the yearly VL incidence data for India and Bangladesh. The proposed model's basic reproduction number ( R 0 ) has been derived and estimated. We have proved the existence of backward bifurcation in our system. The phenomenon of backward bifurcation has public health implications because the classical requirement of R 0 < 1 , while necessary, is no longer sufficient for effective disease control (or elimination). In such a (backward bifurcation) situation, the initial sizes of the model's subpopulations (state variables) would determine the effectiveness of disease control or elimination. As a result, it is the first attempt to represent and study VL disease dynamics using active case detection (ACD) as a control strategy, although a few experimental studies have been conducted to evaluate ACD in disease transmission. We use sensitivity analysis to investigate the effects of the model's controllable parameters for the basic reproduction number. We found that σ 1 , σ 2 , σ 3 (monitoring rate to infected individuals) have negative impacts on R 0 . The numerical result suggests that the ACD strategy can be useful for the VL elimination program. Due to a small increment in the monitoring rate, the dynamic behavior of infected individuals dramatically decreased. Successful employment of ACD strategy may reduce more than 60–80% symptomatic and post kala-azar dermal leishmaniasis (PKDL) individuals. We found that healthcare organizations should prioritize ACD in symptomatic and PKDL individuals over asymptomatic individuals. We also observed that the use of only culling effect to the reservoirs is not beneficial to society in the control of VL, but spraying of insecticides and the use of treated bednets can be effective control strategies to curtail the outbreak of the disease. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model for tuberculosis transmission, which incorporates multiple saturated exogenous reinfections, is proposed and explored. The existence of disease-free and endemic steady states is investigated. Disease-free equilibrium (DFE) is locally asymptotically stable (LAS) but not globally asymptotically stable (GAS) when the basic reproduction number, ℛ 0 < 1. However, it is GAS only when there is no exogenous reinfection. The local asymptotic stability and global asymptotic stability of the unique endemic equilibrium point (EEP) are established under certain conditions when ℛ 0 > 1. Further, the EEP is GAS when ℛ 0 > 1 , provided there is no exogenous reinfection. When ℛ 0 is below unity, the presence of multiple endemic equilibria is found which leads to backward bifurcation. It is demonstrated that the system encounters a Hopf-bifurcation when the transmission rate β crosses a critical value, resulting in the formation of limit cycles, i.e. periodic solutions bifurcate around the EEP when β passes a critical value. The stability and direction of Hopf-bifurcation are also studied. The results of the analytical work are validated through numerical simulations. A numerical simulation illustrates that EEP losses its stability via Hopf-bifurcation for specific parameters. However, when the bifurcation parameter β is increased further, the EEP regains its stability. In addition, Hopf-bifurcation occurs due to exogenous reinfection rates p and . Thus, our model shows some important nonlinear dynamical behaviors. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical threshold stability of a nonlinear age-space structured heroin transmission model. A semi-discrete system is established by spatially domain discretization of the original nonlinear age-space structured model. A threshold value is proposed in stability analysis of the semi-discrete system and named as a numerical basic reproduction number. Besides the role it plays in numerical threshold stability analysis, the numerical basic reproduction number can preserve qualitative properties of the exact basic reproduction number and converge to the latter while stepsizes vanish. A fully discrete system is established via a time discretization of the semi-discrete system, in which an implicit-explicit technique is implemented to ensure the preservation of the biological meanings (such as positivity) without CFL restriction. Some numerical experiments are exhibited in the end to confirm the conclusions and explore the final state. • A numerical scheme is constructed for nonlinear age-structured reaction-diffusion models. • A numerical stability threshold is proposed in numerical stability analysis. • The numerical stability threshold we proposed can preserve qualitative properties of the exact stability threshold. [ABSTRACT FROM AUTHOR]

With the prevalence of online social networks, rumors spread rampantly online. The versatility and complexity of human attitudes make dissemination more challenging to portray, so it is meaningful to develop a more comprehensive diffusion model. To this end, an improved SEIHR model considering three attitudes towards rumors is proposed. Then we deduce the stability of the dynamics model and use two scenarios to validate its accuracy. Meanwhile, rumor diffusion generates extensive social threats. To mitigate such threats, we introduce three immunization strategies and forge bonds among their basic reproduction numbers. Besides, we develop three synergistic optimal controls that vary with the time and degree to impede rumor diffusion. The analysis of the optimal control problem is conducted by Pontryagin's maximum principle. Next, experiments are conducted to verify the efficacy of the SEIHR model and control strategies. Our simulations show that adding the exposed and the hibernated undermines the impact of rumors and puts off terminal time. Additionally, immunization strategies effectively curb rumor diffusion. Moreover, the combination of three synergistic optimal controls leads to the smallest rumor scale and the least cumulative total costs. • An improved SEIHR model is put forward, considering three attitudes toward rumors. • Three immunization strategies are implemented to mitigate social threats. • Three synergistic optimal controls to impede rumor diffusion are implemented. [ABSTRACT FROM AUTHOR]

Temporal synchronization is a relatively common ecological phenomenon in population dynamics. Examples range from annual and biennial plants to Salmon to Cicadas. In discrete-time matrix population models, competition between stages may result in synchronous cycles in which stages are temporally separated. Our work shows how spatial density-dependency dynamics can have a crucial role in population stability through synchronization in a migratory population. Migration is a diverse phenomenon and can be categorized into many forms. The most common type of migration is partial migration, in which some individuals migrate between habitats and others remain in a single habitat during their entire life. We use a discrete stage structure matrix model to investigate which density dependence mechanisms would cause a stable cyclic behavior with alternating and separated generations of juveniles, migrant, and non-migrant adults. We also studied the subsequent adaptive dynamics, which require investigating whether a mutant can invade the dynamic 2-cycle. We also found a dynamic dichotomy between the oscillating 2-cycles and positive equilibria for the partially migrating populations. Using adaptive dynamics and center manifold theory, we showed the existence of an evolutionary stable strategy. We examined how the ideal free distribution (IFD) arises in the context of a temporally separated population. We also show that the ideal free distributions for synchronous 2-cycles are evolutionary stable strategies if migrants and non-migrants experience density-dependent competition with juveniles during reproduction. [ABSTRACT FROM AUTHOR]

The present article investigates a numerical analysis of COVID-19 (temporal and spatio-tempora) lockdown-vaccination models. The proposed models consist of six nonlinear ordinary differential equations as a temporal model and six nonlinear partial differential equations as a spatio-temporal model. The evaluation of reproduction number is a forecast spread of the COVID-19 pandemic. Sensitivity analysis is used to emphasize the importance of pandemic parameters. We show the stability regions of the disease-free equilibrium point and pandemic equilibrium point. We use effective methods such as central finite difference (CFD) and Runge-Kutta of fifth order (RK-5). We apply Von-Neumann stability and consistency of the numerical scheme for the spatio-temporal model. We examine and compare the numerical results of the proposed models under various parameters. [ABSTRACT FROM AUTHOR]

If an infectious disease is eradicated in an area, the travelling of infected people can cause a re-epidemic of the disease in such area. Travelling is one of the inuential factors in the spread of an infectious diseases. In this paper, we present an epidemic model to investigate the effect of travelling between two regions. We compute the basic reproduction number of the model and study the local and global stability of the equilibrium points. In addition, we perform numerical simulations to illustrate the impact of increasing travel parameters on disease dynamics. The results show that travel between areas will change the dynamics of the disease and spread the infection. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an age-structured SIS (susceptible-infectious-susceptible) epidemic model with random diffusion and advection, in which birth and transmission rates depend on individuals. First, the well-posedness of this model was obtained. Next, we established the existence and uniqueness of the nontrivial nonnegative steady state, and derived the basic reproduction number which is also a threshold for the existence of nontrivial nonnegative steady states. Then, we studied the local stability of the nontrivial nonnegative steady state. In particular, we determined the upper and lower bounds of the principal eigenvalue to better obtain the local stability. Finally, we investigated the asymptotic profiles of the principal eigenvalue and the nontrivial nonnegative steady state with respect to diffusion rate and advection rate, respectively. [ABSTRACT FROM AUTHOR]

Optimal use of available resources is one of the major issues in many situations. Apart from this, age is also an important factor in modeling social interaction in a society. In this article, we consider an age‐dependent social interaction model and study the stability and optimal control. Law enforcement is an important factor in controlling crime, and the deployment of police to enforce it is important. Now cost is a major issue, so optimal deployment is very important to study. Stability results are derived in terms of threshold parameters. Basic reproduction number is calculated for stability analysis. Using the adjoint system, the form of the law enforcement factor is obtained in terms of state space variables. We see that the cost functional increases with the increase in the population density of criminal population. Numerical results are also added to visually illustrate our theoretical results. [ABSTRACT FROM AUTHOR]