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Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh–Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R0. If R01, it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for R0 is performed by the method of partial rank correlation coefficient(PRCC).

Abstract Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh–Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if $${R}_{0}1$$ R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if $${R}_{0}1$$ R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter $$\alpha$$ α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

In this paper, we introduce a new mathematical epidemic model with the effect of vaccination. We formulate a Susceptible-High risk-Infective-Recovered-Vaccinated (SHIRV) model in which the susceptible individuals with a higher probability of being infected (H) are selected as a separate class. We study the dynamical behavior of this model and define the basic reproductive number, R0. It is proved that the disease-free equilibrium is asymptotically stable if R0 < 1, and it is unstable if R0 1. Also, we investigate the existence and stability of the endemic equilibrium point analytically. For the system of differential equations of the SHIRV model, we give an approximating solution by using the Legendre-Ritz-Galerkin method. Finally, we study the influence of vaccination on measles and smallpox, two cases of the epidemic, using the proposed method in this paper. Numerical results showed that choosing high-risk people for vaccination can prevent them from getting infected and reduce mortality in the community. [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]

Playing games on mobile devices is one of the most common pastimes in society. The games have got advantages such as reducing stress, providing enjoyment,a sense of chal- lenge and competition, fostering social interaction, and even mental escape from the real world, however negative effect of mobile games on students academic performance is the biggest worry. The control of this worry in the students of secondary schools of Grad 9th at Bannu division, Pakistan, is the studys main focus. We minutly examine the stages of mobile-game addiction. The progression in these stages are represented by differential equations. These coupled differential equations form a mathematical Model. We study different properties of the model including R0, the rate of transmission of game-addiction from one student to the other. Using mathematical techniques, we find the most effective parameters of game-addiction and intervene therein to design control strategies to stop further transmission of game-addiction. The results and recommendations obtained from these strategies are validated with help of numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we propose a cholera model to study the effects of multiple transmission pathways, imperfect vaccine, nonlinear incidences, and differential infectivity of vibrios. The expression of the basic reproductive number R 0 is derived. There is only the disease-free equilibrium E 0 if R 0 ≤ 1 , while, besides E 0 , there is also a unique endemic equilibrium E ∗ if R 0 > 1 . When R 0 < 1 , E 0 is globally asymptotically stable by using the technique of linearization and the fluctuation lemma. When R 0 > 1 , E ∗ is globally asymptotically stable by the Lyapunov direct method. These theoretical results are supported with numerical simulations for the case with Beddington-DeAngelis incidences. We further perform the sensitivity analyses of R 0 and the infection level at E ∗ to determine the significant parameters affecting disease outbreak and severity, respectively. Influences of the vaccination rate ϕ and the waning rate of vaccine η on the dynamical behaviors of the model are also discussed. [ABSTRACT FROM AUTHOR]

In this study, we developed and analyzed a compartmental epidemic model and a system model that incorporate vaccination, elimination, and quarantine techniques, with a saturated incidence rate, by theoretical and numerical means. The model is described by a system of four nonlinear differential equations. Our analysis included determining the reproduction number Rq and examining equilibrium solutions. The outcomes of the disease are identified through the threshold Rq. When Rq1, the unique endemic equilibrium is asymptotically stable locally. The stability of the endemic and disease-free equilibria globally has been examined using the Routh–Hurwitz and Dulac criteria. Subsequently, numerical simulations were utilized to illustrate the theoretical findings effectively.

This work introduces the Queen's University Agent-Based Outbreak Outcome Model (QUABOOM). This tool is an agent-based Monte Carlo simulation for modelling epidemics and informing public health policy. We illustrate the use of the model by examining capacity restrictions during a lockdown. We find that public health measures should focus on the few locations where many people interact, such as grocery stores, rather than the many locations where few people interact, such as small businesses. We also discuss a case where the results of the simulation can be scaled to larger population sizes, thereby improving computational efficiency.

The main goal of this work was to propose a novel mathematical model for malware propagation on wireless sensor networks (WSN). Specifically, the proposed model was a compartmental and global one whose temporal dynamics were described by means of a system of ordinary differential equations. This proposal was more realistic than others that have appeared in the scientific literature since. On the one hand, considering the specifications of malicious code propagation, several types of nodes were considered (susceptible, patched susceptible, latent non-infectious, latent infectious, compromised non-infectious, compromised infectious, damaged, ad deactivated), and on the other hand, a new and more realistic term of the incidence was defined and used based on some particular characteristics of transmission protocol on wireless sensor networks.

ABSTRACT Background: Onchocerciasis infection is one of the neglected tropical diseases targeted for eradication by 2030. The disease is usually transmitted to humans through the bites of black flies. These black flies mostly breed near well-oxygenated fast-running water bodies. The disease is common in mostly remote agricultural villages near rivers and streams.Objective: In this study, a deterministic model describing the infection dynamics of human onchocerciasis disease with control measures is presented.Methods: We derived the model’s reproductive number and used a stability theorem of a Metzler matrix to show that disease-free equilibrium is both locally and globally asymptotically stable whenever the reproductive number is less than one. Parameter contribution was conducted using sensitivity analysis. The model endemic equation is shown to be a cubic polynomial in the presence of infected immigrants and a quadratic form in their absence.Results: When the inflow of infected immigrants is null, the model endemic equation may admit a unique equilibrium if the reproductive number is greater than one, or admits multiple endemic equilibria if the reproductive number is less than unity. We carried out a sensitivity analysis to identify the significant parameters that contribute to onchocerciasis spread.Conclusion: Onchocerciasis disease can be eradicated if the importation of infected immigrants is properly monitored. The integration of the One Health concept in the public health system is key in tackling the emergence and spread of diseases.

This work introduces the Queen's University Agent-Based Outbreak Outcome Model (QUABOOM). This tool is an agent-based Monte Carlo simulation for modelling epidemics and informing public health policy. We illustrate the use of the model by examining capacity restrictions during a lockdown. We find that public health measures should focus on the few locations where many people interact, such as grocery stores, rather than the many locations where few people interact, such as small businesses. We also discuss a case where the results of the simulation can be scaled to larger population sizes, thereby improving computational efficiency. [ABSTRACT FROM AUTHOR]

We investigate the dynamic behaviors of a discrete-time SIR epidemic model under intervention. Specifically, we examine the effects of reducing contacts among individuals at a particular time iii by a factor of q > 1, such that 96/q < 1. Our analysis reveals that in this case. the final size of the epidemic can be approximated by the formula Rm Ro (1 - 1/q)/(1 - Ro/q), where RIll denotes the cumulative number of cases at date m and *D is the basic reproductive number. We also explore the situation where contacts are entirely eliminated at an early stage of the epidemic, i.e. when q -* oo. Our results indicate that in such cases, the final size of the epidemic can be estimated by multiplying the cumulative number of cases Rm at that date by the basic reproductive number: RD. Our study provides valuable insights intO the effectiveness of intervention strategies in controlling the spread of infectious diseases. We anticipate that our findings will be of interest to researchers, policymakers. and public health officials. [ABSTRACT FROM AUTHOR]

The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system's equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health. [ABSTRACT FROM AUTHOR]

This paper establishes a novel fractional-order version of a recently expanded form of the Susceptible-Exposed-Infectious-Recovery (SEIR) Mpox model. This model is investigated by means of demonstrating some significant findings connected with the stability analysis and the vaccination impact, as well. In particular, we analyze the fractional-order Mpox model in terms of its invariant region, boundedness of solution, equilibria, basic reproductive number, and its elasticity. In accordance with an effective vaccine, we study the progression and dynamics of the Mpox disease in compliance with various scenarios of the vaccination ratio through the proposed fractional-order Mpox model. Accordingly, several numerical findings of the proposed model are depicted with the use of two numerical methods; the Fractional Euler Method (FEM) and Modified Fractional Euler Method (MFEM). Such findings demonstrate the influence of the fractional-order values coupled with the vaccination rate on the dynamics of the established disease model. [ABSTRACT FROM AUTHOR]

In the endeavor to halt the transmission of infectious diseases, containment and isolation emerge as pivotal preventive strategies. The elucidation of disease spread dynamics, through the lens of mathematical models, is instrumental in forecasting epidemiological trajectories. This study presents an augmented Susceptible-Infected-Recovered (SIR) model, assimilating these preventive measures, to scrutinize the propagation of COVID-19 since its initial emergence. The combat against this pandemic has predominantly hinged upon non-pharmaceutical interventions (NPIs) including, but not limited to, mask utilization, physical distancing, patient isolation, contact quarantine, and hand hygiene. The focal point of our investigation lies in the examination of the influence of susceptible population containment and infected individual isolation on the evolution of the ongoing outbreak. The basic reproductive number, an indicator of contagiousness, is analyzed over the course of the outbreak, yielding promising outcomes. [ABSTRACT FROM AUTHOR]

Epidemic diseases and media campaigns are closely associated with each other. Considering most epidemics have multiple pathogenic strains, in this paper, we take the lead in proposing two multi-strain SIS epidemic models in heterogeneous networks incorporating awareness programs due to media. For the first model, we assume that the transmission rates for strain 1 and strain 2 depend on the level of awareness campaigns. For the second one, we further suppose that awareness divides susceptible population into two different subclasses. After defining the basic reproductive numbers for the whole model and each strain, we obtain the analytical conditions that determine the extinction, coexistence and absolute dominance of two strains. Moreover, we also formulate its optimal control problem and identify an optimal implementation pair of awareness campaigns using optimal control theory. Given the complexity of the second model, we use the numerical simulations to visualize its different types of dynamical behaviors. Through theoretical and numerical analysis of these two models, we discover some new phenomena. For example, during the persistence analysis of the first model, we find that the characteristic polynomials of two boundary equilibria may have a pair of pure imaginary roots, implying that Hopf bifurcation and periodic solutions may appear. Most strikingly, multistability occurs in the second model and the growth rate of awareness programs (triggered by the infection prevalence) has a multistage impact on the final size of two strains. The numerical results suggest that the spread of a two-strain epidemic can be controlled (even be eradicated) by taking the measures of enhancing awareness transmission, reducing memory fading of aware individuals and ensuring high-level influx and rapid growth of awareness programs appropriately. [ABSTRACT FROM AUTHOR]

Abstract SARS-COV-2 is responsible for the current worldwide pandemic, which started on December 2019 in Wuhan, China. On March 2020 World Health Organization announced COVID-19 as the new pandemic. Some SARS-COV-2 variants have increased transmissibility, cause more severe disease (e.g., increased hospitalizations or deaths), are resistant to antibodies produced by the previous infection or vaccination, and there is more difficulty in treatment and diagnosis of them. World Health Organization considered them as SARS-CoV-2 variants of concern. The introductory reproduction rate (R 0) is an epidemiologic index of the transmissibility of the virus, defined as the average number of persons infected by the virus after known contact with an infectious person in a susceptible population. An R 0 > 1 means that the virus is spreading exponentially, and R 0

This work attempts to study the numerical solution of nonlinear delayed Immunized Susceptible Latent Infected and Recovered (MSLIR) epidemic model of HBV disease. Reproduction number, equilibria and stability are discussed. Three different numerical techniques, Euler, RK-4 and the non-standard finite difference (NSFD) techniques are used for the numerical solution of the model. The proposed technique is independent of the size of the time step, while forward Euler and RK-4 depend on the size of a time step and retains all essential characteristics of the continuous MSLIR epidemic model like positivity and stability of equilibrium, while well-known forward Euler and RK-4 cannot sustain these characteristics. Therefore, the proposed (NSFD) technique becomes a more efficient and reliable numerical technique than the forward Euler and RK-4 scheme. Numerical simulations are presented for the validation of the obtained results.

Cassava mosaic disease (CMD) is caused by a virus transmitted by the whitefly. This disease can destroy cassava at any stage of its growth and it resulted in lower cassava yields. In this paper, we developed a mathematical model for the epidemic of cassava mosaic disease with a deterministic model which has saturation incidence rates. This model aims to explain the effect of vectors on cassava disease outbreaks. First, this model was analyzed using standard dynamic methods to determine the behavior of the solution. We found the existence and condition of disease-free and endemic steady state. The basic reproductive number ($ R_0 $) is obtained by using the next-generation method which $ R_0 $ helps assess the ability to spread infectious diseases. Second, the stability of the steady state was analyzed, then we obtain the condition of existence of local stability and global stability at each steady state of this model. Third, analysis of the sensitivity indices in the threshold number to determine the effect of the various parameters. Finally, the results of the theoretical model were validated by numerical simulations. It is represented by various graphs converging at a steady state and stable.

This paper is devoted to a nonlocal SIR type epidemic model, with free boundary denoting the expanding front. We aim to examine the full information about the dynamical behaviors of the involved disease that caused by the nonlocal diffusion and growing habitat. We obtain a classification for the spreading and vanishing cases, and show that those are determined by the new proposed threshold function R0F(t) and especially the corresponding initial data R0F(0). We prove that R0F(t)≤R0 and R0F(t)→R0 as t tends to ∞, R0 here representing the basic reproductive number of the associated ordinary differential equation. Also, the result show that the introduce of the nonlocal diffusion makes the disease becomes more easier to spread. In addition, we present some numerical simulations to confirm the theoretical results, as well as the impacts of R0 and the expanding capability.

A compartmental model is considered to study the transmission dynamics of COVID-19. The proposed model is investigated for different results by using Volterra-Lyapunov (V-L) matrix theory. In this regard, first we presented a modified form of SEIR model by incorporating three new compartments C (protected), D (death due to corona) and Q (quarantined). Both equilibrium points are computed together with basic reproductive number. In addition, local stability of both equilibrium points for our proposed model is examined by assuming that wearing of mask, testing of the unaware infected individuals and medical care of the individuals that got infected should constantly be maintained. Hence, subsequently by combining the V-L stable matrix theory with the traditional methodology of constructing the Lyapunov functions, a procedure for the global stability analysis of COVID-19 is presented. Furthermore, based on LaSalle and Lipschitz invariance principle, the global stability of disease free equilibrium point is also examined. The technique we introduced in this paper will provide the more profound comprehension to understand the basic structure of COVID-19. Moreover, for numerical interpretation of our proposed model non-standard finite difference (NSFD) scheme is utilized for simulations. Different graphical illustrations are provided to understand the transmission dynamics.

Marital instability has a devastating effect on our society. In general, marital disruption results in negative physical and psychological health outcomes, as well as adverse economic consequences for children, adolescents and adults. An all-interactive bi-disruption state model is proposed and the stability of the disruption-free equilibrium of the model is explored. The aim is to examine the effects of both homogenous and heterogenous interactions on the propagation potential (the basic reproductive number) of marital disruptions. The homogenous interaction epitomizes couples’ own interaction in the marriage, while heterogenous interactions represent couples’ interactions with individuals of other unstable states. Stability analysis of the marital disruption-free equilibrium was established using both the Routh Stability and Castilos-Chavez GAS criteria. It was revealed that the marital disruption-free is locally and globally asymptotically stable whenever the basic reproductive number is less than unity. The dynamics were further demonstrated through sensitivity analysis of the parameters using the RK4 simulation technique, achieved with codes implemented in R. As the simulation results evince, increases of 33% and 17% in the rates of homogenous resolution and remarriage, as well as 13% and 15% decreases in the rates of heterogenous contacts respectively between individuals of states M and P; and M and D are enough to ensure stability of marriages. The study therefore, has crucial guidelines to minimize marital instability.

Maturation strategies play a key role in the survival and development of populations. In response to changes in the external environment and human interventions, populations adopt appropriate maturation strategies. Different maturation strategies can lead to different birth and mortality rates. In this paper, we develop and analyze a stage-structured population model with two maturation strategies to obtain conditions for the coexistence of two maturation strategies and conditions for competitive exclusion. Our results also show that equality of fitness—represented by basic reproductive numbers being greater than 1 under different maturation strategies—promotes the coexistence of the two strategies. The reason why a strategy is replaced by another one is that the population adopting this strategy has weak fitness, which is measured by the basic reproductive number. [ABSTRACT FROM AUTHOR]

Species interaction networks, which play an important role in determining pathogen transmission and spread in ecological communities, can shift in response to agricultural landscape simplification. However, we know surprisingly little about how landscape simplification-driven changes in network structure impact epidemiological patterns. Here, we combine mathematical modelling and data from eleven bipartite plant-pollinator networks observed along a landscape simplification gradient to elucidate how changes in network structure shape disease dynamics. Our empirical data show that landscape simplification reduces pathogen prevalence in bee communities via increased diet breadth of the dominant species. Furthermore, our empirical data and theoretical model indicate that increased connectance reduces the likelihood of a disease outbreak and decreases variance in prevalence among bee species in the community, resulting in a dilution effect. Because infectious diseases are implicated in pollinator declines worldwide, a better understanding of how land use change impacts species interactions is therefore critical for conserving pollinator health.

Among many epidemic prevention measures, isolation is an important method to control the spread of infectious disease. Scholars rarely study the impact of isolation on disease dissemination from a quantitative perspective. In this paper, we introduce an isolation ratio and establish the corresponding model. The basic reproductive number and its biological explanation are given. The stability conditions of the disease-free and endemic equilibria are obtained by analyzing its distribution of characteristic values. It is shown that the isolation ratio has an important influence on the basic reproductive number and the stability conditions. Taking the COVID-19 in Wuhan as an example, isolating more than 68% of the population can control the spread of the epidemic. This method can provide precise epidemic prevention strategies for government departments. Numerical simulations verify the effectiveness of the results.

SARS-COV-2 is responsible for the current worldwide pandemic, which started on December 2019 in Wuhan, China. On March 2020 World Health Organization announced COVID-19 as the new pandemic. Some SARS-COV-2 variants have increased transmissibility, cause more severe disease (e.g., increased hospitalizations or deaths), are resistant to antibodies produced by the previous infection or vaccination, and there is more difficulty in treatment and diagnosis of them. World Health Organization considered them as SARS-CoV-2 variants of concern. The introductory reproduction rate (R0) is an epidemiologic index of the transmissibility of the virus, defined as the average number of persons infected by the virus after known contact with an infectious person in a susceptible population. An R0 > 1 means that the virus is spreading exponentially, and R0 < 1, means that the outbreak is subsiding. In various studies, the estimated R and VOC growth rates were reported to be greater than the ancestral strains. However, it was also a low level of concordance between the estimated Rt of the same variant in different studies. It is because the R of a variant not only dependent on the biological and intrinsic factors of the virus but also several parameters can affect the R0, including the duration of contagiousness and the likelihood of infection per contact. Evaluation of changes in SARS-CoV-2 has shown that the rate of human-to-human transmission of this virus has increased. Like other viruses with non-human sources which succeeded in surviving in the human population, SARS-CoV-2 has gradually adapted to the human population, and its ability to transmit from human to human has increased. Of course, due to the continuous changes in this virus, it is crucial to survey the rate of transmission of the virus over time. [ABSTRACT FROM AUTHOR]

This work attempts to study the numerical solution of nonlinear delayed Immunized Susceptible Latent Infected and Recovered (MSLIR) epidemic model of HBV disease. Reproduction number, equilibria and stability are discussed. Three different numerical techniques, Euler, RK-4 and the non-standard finite difference (NSFD) techniques are used for the numerical solution of the model. The proposed technique is independent of the size of the time step, while forward Euler and RK-4 depend on the size of a time step and retains all essential characteristics of the continuous MSLIR epidemic model like positivity and stability of equilibrium, while well-known forward Euler and RK-4 cannot sustain these characteristics. Therefore, the proposed (NSFD) technique becomes a more efficient and reliable numerical technique than the forward Euler and RK-4 scheme. Numerical simulations are presented for the validation of the obtained results. [ABSTRACT FROM AUTHOR]

Large gatherings of people on cruise ships and warships are often at high risk of COVID-19 infections. To assess the transmissibility of SARS-CoV-2 on warships and cruise ships and to quantify the effectiveness of the containment measures, the transmission coefficient (β), basic reproductive number (R 0), and time to deploy containment measures were estimated by the Bayesian Susceptible-Exposed-Infected-Recovered model. A meta-analysis was conducted to predict vaccine protection with or without non-pharmaceutical interventions (NPIs). The analysis showed that implementing NPIs during voyages could reduce the transmission coefficients of SARS-CoV-2 by 50%. Two weeks into the voyage of a cruise that begins with 1 infected passenger out of a total of 3,711 passengers, we estimate there would be 45 (95% CI:25-71), 33 (95% CI:20-52), 18 (95% CI:11-26), 9 (95% CI:6-12), 4 (95% CI:3-5), and 2 (95% CI:2-2) final cases under 0%, 10%, 30%, 50%, 70%, and 90% vaccine protection, respectively, without NPIs. The timeliness of strict NPIs along with implementing strict quarantine and isolation measures is imperative to contain COVID-19 cases in cruise ships. The spread of COVID-19 on ships was predicted to be limited in scenarios corresponding to at least 70% protection from prior vaccination, across all passengers and crew. [ABSTRACT FROM AUTHOR]

To explore malware propagation mechanisms in networks and to develop optimal strategies for controlling the spread of malware, we propose a susceptible-unexposed-infected-isolation-removed epidemic model. First, we establish a non-linear dynamic equation of malware propagation. Then, the basic reproductive number is derived by using the next-generation method. Finally, we carry out numerical simulations to observe the malware spreading in WSNs to verify the obtained theoretical results. Furthermore, we investigate the communication range of the nodes to make the results more complete. The optimal range of the nodes is designed to control malware propagation.

How a disease is transmitted affects our ability to determine R₀, the average number of new cases caused by an infectious host at the onset of an epidemic. R₀ becomes progressively more difficult to compute as transmission varies from directly transmitted diseases to diseases that are vector-borne to environmentally transmitted diseases. Pathogens responsible for diseases with environmental transmission are typically maintained in environmental reservoirs that exhibit a complex spatial distribution of local infectious zones (LIZs). Understanding host encounters with LIZs and pathogen persistence within LIZs is required for an accurate R₀ and modeling these contacts requires an integrated geospatial and dynamical systems approach. Here we review how interactions between host and pathogen populations and environmental reservoirs are driven by landscape-level variables, and synthesize the quantitative framework needed to formulate outbreak response and disease control.

ABSTRACT: Background: Tuberculosis (TB) is one of the top 10 causes of death worldwide. The World Health Organization adopted the ‘End TB Strategy’ to end the global TB epidemic by 2035. However, achieving this goal will be difficult using current measures. Methods: A Susceptible-Exposed-Infectious-Recovered (SEIR) model that distinguishes drug-sensitive (DS) and drug-resistant (DR) TB in the entire Chinese population was established. Goodness-of-fit tests and sensitivity analyses were used to assess model performance. Predictive analysis was performed to assess the effect of different prevention and control strategies on DR-TB. Results: We used parameter fitting to determine the basic reproduction number of the model as R0 = 0.6993. The predictive analysis led to two major projections that can achieve the goal by 2035. First, if the progression rate of latently infected people reaches 10%, then there will be 92.2% fewer cases than in 2015. Second, if the cure rate of DR-TB increases to 40%, then there will be 91.5% fewer cases than in 2015. A combination of five interventions could lead to earlier achievement of the 2035 target. Conclusion: We found that reducing the probability of transmission and the rate of disease progression in patients with DR-TB and improving treatment compliance and the cure rate of patients with DR-TB can contribute to attaining the goal of the End TB Strategy.

In this work we present a general framework for the modeling of the transmission dynamics of macroparasites which do not reproduce within the host like Ascaris lumbricoides, Trichuris trichiura, Necator americanus y Ancylostoma duodenale. The basic models are derived from general probabilistic models for the parasite density-dependent mating probability. Here we considered the particular, and common case, of a negative binomial distribution for the number of parasites in hosts. We find the basic reproductive number and we show that the system exhibits a saddle-node bifurcation at some value of the basic reproduction number. We also found the equilibria and basic reproduction number of a model for the more general case of heterogeneous host populations. [ABSTRACT FROM AUTHOR]

We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes. [ABSTRACT FROM AUTHOR]

In this paper, we use delay differential equations to propose a mathematical model for COVID-19 therapy with both defective interfering particles and artificial antibodies. For this model, the basic reproduction number [Math Processing Error] R 0 is given and its threshold properties are discussed. When [Math Processing Error] R 0 < 1 , the disease-free equilibrium [Math Processing Error] E 0 is globally asymptotically stable. When [Math Processing Error] R 0 > 1 , [Math Processing Error] E 0 becomes unstable and the infectious equilibrium without defective interfering particles [Math Processing Error] E 1 comes into existence. There exists a positive constant [Math Processing Error] R 1 such that [Math Processing Error] E 1 is globally asymptotically stable when [Math Processing Error] R 1 < 1 < R 0. Further, when [Math Processing Error] R 1 > 1 , [Math Processing Error] E 1 loses its stability and infectious equilibrium with defective interfering particles [Math Processing Error] E 2 occurs. There exists a constant [Math Processing Error] R 2 such that [Math Processing Error] E 2 is asymptotically stable without time delay if [Math Processing Error] 1 < R 1 < R 0 < R 2 and it loses its stability via Hopf bifurcation as the time delay increases. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions. [ABSTRACT FROM AUTHOR]

Pandemics, such as Covid-19 and AIDS, tend to be highly contagious and have the characteristics of global spread and existence of multiple virus strains. To analyze the competition among different strains, a high dimensional SIR model studying multiple strains' competition in patchy environments is introduced in this work. By introducing the basic reproductive number of different strains, we found global stability conditions of disease-free equilibrium and persistence conditions of the model. The competition exclusion conditions of that model are also given. This work gives some insights into the properties of the multiple strain patchy model and all of the analysis methods used in this work could be used in other related high dimension systems.

At the end of 2019 the mankind had to face a new coronavirus infection with higher virulence which resulted in its rapid spread all over the world and in an ultimate pandemic. Initially a new virus which causes COVID-19 was called 2019-nCoV but it soon acquired its well-known name, SARS-CoV-2. We can positively state that this new coronavirus infection will remain in the history of world public healthcare as a disease that caused a collapse in rendering medical aid. Undoubtedly, this new coro-navirus infection has changed customary lifestyle of the overall world population. This review can be considered problematic in its essence and focuses on examining contemporary trends in the official epidemiologic situation in the world regarding the new coronavirus infection (SARS-CoV-2). Having analyzed several foreign and domestic documents, the authors revealed a necessity to enhance levels and quality of COVID-19 epidemiologic diagnostics. There is a suggestion being considered at the moment on including additional clinical and diagnostic activities aimed at preventing further spread of the new coronavirus infection. We should note that data on COVID-19-related mortality and morbidity are renewed every day and every hour. Given that, it seems rather difficult to keep in line with the latest trends in COVID-19 prevention and epidemiologic diagnostics. However, the authors made an attempt to possibly collect all the latest data on epidemiological peculiarities related to the clinical course of the new coronavirus infection. The authors have a hope that this review will be useful for epidemiologists when they detect new cases of the disease as well as for lecturers at medical higher educational establishments when they train students and resident physicians.

The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system’s equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health.

This paper establishes a novel fractional-order version of a recently expanded form of the Susceptible-Exposed-Infectious-Recovery (SEIR) Mpox model. This model is investigated by means of demonstrating some significant findings connected with the stability analysis and the vaccination impact, as well. In particular, we analyze the fractional-order Mpox model in terms of its invariant region, boundedness of solution, equilibria, basic reproductive number, and its elasticity. In accordance with an effective vaccine, we study the progression and dynamics of the Mpox disease in compliance with various scenarios of the vaccination ratio through the proposed fractional-order Mpox model. Accordingly, several numerical findings of the proposed model are depicted with the use of two numerical methods; the Fractional Euler Method (FEM) and Modified Fractional Euler Method (MFEM). Such findings demonstrate the influence of the fractional-order values coupled with the vaccination rate on the dynamics of the established disease model.

Abstract Background The first confirmed cases of COVID-19 in Iran were reported in Qom city. Subsequently, the neighboring provinces and gradually all 31 provinces of Iran were involved. This study aimed to investigate the case fatility rate, basic reproductive number in different period of epidemic, projection of daily and cumulative incidence cases and also spatiotemporal mapping of SARS-CoV-2 in Alborz province, Iran. Methods A confirmed case of COVID-19 infection was defined as a case with a positive result of viral nucleic acid testing in respiratory specimens. Serial interval (SI) was fitted by gamma distribution and considered the likelihood-based R0 using a branching process with Poisson likelihood. Seven days average of cases, deaths, doubling times and CFRs used to draw smooth charts. kernel density tool in Arc GIS (Esri) software has been employed to compute hot spot area of the study site. Results The maximum-likelihood value of R0 was 2.88 (95%, CI: 2.57–3.23) in the early 14 days of epidemic. The case fatility rate for Alborz province (Iran) on March 10, was 8.33% (95%, CI:6.3–11), and by April 20, it had an increasing trend and reached 12.9% (95%,CI:11.5–14.4). The doubling time has been increasing from about two days and then reached about 97 days on April 20, 2020, which shows the slowdown in the spread rate of the disease. Also, from March 26 to April 2, 2020 the whole Geographical area of Karj city was almost affected by SARS-CoV-2. Conclusions The R0 of COVID-19 in Alborz province was substantially high at the beginning of the epidemic, but with preventive measures and public education and GIS based monitoring of the cases,it has been reduced to 1.19 within two months. This reduction highpoints the attainment of preventive measures in place, however we must be ready for any second epidemic waves during the next months.

Extrinsic environmental factors influence the spatiotemporal dynamics of many organisms, including insects that transmit the pathogens responsible for vector‐borne diseases (VBDs). Temperature is an especially important constraint on the fitness of a wide variety of ectothermic insects. A mechanistic understanding of how temperature impacts traits of ectotherms, and thus the distribution of ectotherms and vector‐borne infections, is key to predicting the consequences of climate change on transmission of VBDs like malaria. However, the response of transmission to temperature and other drivers is complex, as thermal traits of ectotherms are typically nonlinear, and they interact to determine transmission constraints. In this study, we assess and compare the effect of temperature on the transmission of two malaria parasites, Plasmodium falciparum and Plasmodium vivax, by two malaria vector species, Anopheles gambiae and Anopheles stephensi. We model the nonlinear responses of temperature dependent mosquito and parasite traits (mosquito development rate, bite rate, fecundity, proportion of eggs surviving to adulthood, vector competence, mortality rate, and parasite development rate) and incorporate these traits into a suitability metric based on a model for the basic reproductive number across temperatures. Our model predicts that the optimum temperature for transmission suitability is similar for the four mosquito–parasite combinations assessed in this study, but may differ at the thermal limits. More specifically, we found significant differences in the upper thermal limit between parasites spread by the same mosquito (A. stephensi) and between mosquitoes carrying P. falciparum. In contrast, at the lower thermal limit the significant differences were primarily between the mosquito species that both carried the same pathogen (e.g., A. stephensi and A. gambiae both with P. falciparum). Using prevalence data, we show that the transmission suitability metric ST$$ S(T) $$ calculated from our mechanistic model is consistent with observed P. falciparum prevalence in Africa and Asia but is equivocal for P. vivax prevalence in Asia, and inconsistent with P. vivax prevalence in Africa. We mapped risk to illustrate the number of months various areas in Africa and Asia predicted to be suitable for malaria transmission based on this suitability metric. This mapping provides spatially explicit predictions for suitability and transmission risk. [ABSTRACT FROM AUTHOR]

Since the outbreak of African swine fever (ASF) in Shengyang, it has continued spreading in China. In the early stage of the epidemic, multi‐point and concentrated outbreaks were mainly in the swill feeding areas. In this paper, we developed compartmental models to investigate the transmission of ASF in several raising units including Guquan, Jinba and Liancheng. Using the data collected from these three infected premises, we calibrated the models to estimate that the average incubation period was between 8 and 11 days, the onset period was about 2–3 days and the basic reproductive number was about 4.83–11.90. We also estimated the infection on the day before culling to be 45.24% (Guquan), 89.20% (Jinba) and 16.35% (Liancheng), respectively. The infection rate of Guquan could reach about 74.8% if culling were postponed by 2 days. We found that the infection was significantly higher than the morbidities (22.11% (Guquan), 49.35% (Jinba) and 12.94% (Liancheng)) calculated by actual statistical data. Besides, we simulated and compared the control effect of stopping transport, disinfecting, stopping swill and culling. Our findings suggest that any single measure was not enough to prevent the spread of ASF on a regional level but the combined measures is the key. Under the current situation, fully culling was recognized as most effective in controlling the epidemic, despite the culling of uninfected pigs. [ABSTRACT FROM AUTHOR]

Humanity has suffered throughout its history from different types of pandemics caused by deadly infectious diseases. Mathematical models are very useful tools to understand the dynamics of the behavior and propagation of these. Among these models are those known as SIS, SIR and SEIR. This paper presents a brief explanation of the structure of these models and its use in some pandemics. In particular, some SIR-type models without and with delays are analyzed with special interest, as well as their applications to the current pandemic caused by the SARS-CoV-2 virus. To determine the correspondence between some of the models analyzed and the data of Infectious and Recovered from Mexico reported by the World Health Organization (WHO), simulations are presented in three different time periods between the years 2020-2021. In addition, an unpublished SIR-type mathematical model with three delays is proposed as a main contribution. Finally, a discussion is given on the application of numerical algorithms to identify some parameters of mathematical models, such as ordinary least squares. [ABSTRACT FROM AUTHOR]