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Malaria, a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes, remains a significant public health concern, claiming over 600,000 lives annually, predominantly among children. Novel tools, including the application of Wolbachia, are being developed to combat malaria-transmitting mosquitoes. This study presents a modified susceptible-exposed-infectious-recovered-susceptible (SEIRS) compartmental mathematical model to evaluate the impact of awareness-based control measures on malaria transmission dynamics, incorporating mosquito interactions and seasonality. Employing the next-generation matrix approach, we calculated a basic reproduction number (R0) of 2.4537, indicating that without robust control measures, the disease will persist in the human population. The model equations were solved numerically using fourth and fifth-order Runge-Kutta methods. The model was fitted to malaria incidence data from Kenya spanning 2000 to 2021 using least squares curve fitting. The fitting algorithm yielded a mean absolute error (MAE) of 2.6463 when comparing the actual data points to the simulated values of infectious human population (Ih). This finding indicates that the proposed mathematical model closely aligns with the recorded malaria incidence data. The optimal values of the model parameters were estimated from the fitting algorithm, and future malaria dynamics were projected for the next decade. The research findings suggest that social media-based awareness campaigns, coupled with specific optimization control measures and effective management methods, offer the most cost-effective approach to managing malaria.

Malaria, a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes, remains a significant public health concern, claiming over 600,000 lives annually, predominantly among children. Novel tools, including the application of Wolbachia, are being developed to combat malariatransmitting mosquitoes. This study presents a modified susceptible-exposed-infectious-recovered-susceptible (SEIRS) compartmental mathematical model to evaluate the impact of awareness-based control measures on malaria transmission dynamics, incorporating mosquito interactions and seasonality. Employing the next-generation matrix approach, we calculated a basic reproduction number (R0) of 2.4537, indicating that without robust control measures, the disease will persist in the human population. The model equations were solved numerically using fourth and fifth-order Runge-Kutta methods. The model was fitted to malaria incidence data from Kenya spanning 2000 to 2021 using least squares curve fitting. The fitting algorithm yielded a mean absolute error (MAE) of 2.6463 when comparing the actual data points to the simulated values of infectious human population (Ih). This finding indicates that the proposed mathematical model closely aligns with the recorded malaria incidence data. The optimal values of the model parameters were estimated from the fitting algorithm, and future malaria dynamics were projected for the next decade. The research findings suggest that social media-based awareness campaigns, coupled with specific optimization control measures and effective management methods, offer the most cost-effective approach to managing malaria. [ABSTRACT FROM AUTHOR]

This study aimed to develop a Suspected-Exposed-Infected-Recovered (SEIRS) mathematical model to solve addiction to online games. The model would use optimal control to analyze and predicts addiction cases among the State Junior High School students. The model was analyzed through determination of the equilibrium point, stability, and basic reproduction number (R0). The optimal control problem was solved using the Pontryagin principle to minimize the number of addicted groups. The analysis without control gave an initial value of R0 = 1.94 > 1, which indicated that online game addiction in students at a worrying level. The value R0 with 1% control was R0 = 1.892, which showed that the problem is still worrying. Meanwhile, 50% and 90% controls gave R0 = 0.814 and R0 = 0.556, respectively, which indicated that the problems can be overcome because the values are less than one. This shows that the greater the control, the lower the transmission rate for online game addiction. [ABSTRACT FROM AUTHOR]

Lumpy skin disease (LSD) is an economically significant viral disease of cattle caused by the lumpy disease virus (LSDV) which is primarily spread mechanically by blood feeding vectors such as particular species in flies, mosquitoes and ticks. Despite efforts to control its spread, LSD has been expanding geographically, posing challenges for effective control measures. This study develops a Susceptible–Exposed–Infectious–Recovered–Susceptible (SEIRS) model that incorporates cattle and vector populations to investigate LSD transmission dynamics. The model considers the waning rate of natural active immunity in recovered cattle, disease-induced mortality, and the biting rate. Using a standard dynamical system approach, we conducted a qualitative analysis of the model, defining the invariant region, establishing conditions for solution positivity, computing the basic reproduction number, and examining the stability of disease-free and endemic equilibria. We employ a non-linear least squares method for model calibration, fitting it to a synthetic dataset. We subsequently test it with actual infectious cases data. Results from the calibration and testing phases demonstrate the model’s validity and reliability for diverse settings. Local and global sensitivity analyses were conducted to determine the model’s robustness to parameter values. The biting rate emerged as the most significant parameter, followed by the probabilities of infection from either population and the recovery rate. Additionally, the waning rate of LSD infection-induced immunity gained positive significance in LSD prevalence from the beginning of the infectious period onward. Simulation results suggest reducing the biting rate as the most effective LSD control measure, which can be achieved by applying vector repellents in cattle farms/herds, thereby mitigating the disease’s prevalence in both cattle and vector populations and reducing the chances of infection from either population. Furthermore, measures aiming to boost LSD infection-induced immunity upon recovery are recommended to preserve the immune systems of the cattle population.

(1) Background: The spread of agricultural green production technologies and systems among small farmers is affected by multiple factors such as subjectivity and objectivity. (2) Methods: Based on the marketability of agricultural green production socialization services (AGPSSs), this paper constructs a SEIRS model of infectious disease dynamics, taking the AGPSS of "MAP Sinochem Modern Agriculture" in Tianshan Town, Arhorchin Banner as an example. (3) Results: This study uses Python to simulate the process of forming a network of AGPSS for small farmers and analyzes the law of information dissemination among farmers. (4) Conclusions: This paper explores how multiple factors such as service quality, external environment, farmers' willingness to decide, government guidance and the responsibility of service subjects play roles in the formation and diffusion of an AGPSS network so as to improve the quality and level of AGPSS provided by enterprises. [ABSTRACT FROM AUTHOR]

We discuss a few variations of the SEIRS epidemic model. How basic dynamical properties of the models can be derived by using some tools of the computer algebra system Mathematica is shown, and how invariant surfaces of the system can be found by using computer algebra system Singular is explained. Some numerical simulations are presented as well. [ABSTRACT FROM AUTHOR]

We developed a mathematical model to study the effects of non-pharmaceutical interventions (NPIs) on the dynamics of an epidemic. The level of intervention was assessed as a fraction of the population being isolated and depended on the level of incidence of the epidemic in the population. We performed a mathematical analysis of the model and showed that, depending on the choice of the prevalence-dependent isolation function, it is possible to create new endemic equilibria and to change the stability of the disease-free equilibrium for which the epidemic vanishes. The model was then applied to the case of the COVID-19 pandemic. Several NPI management strategies were considered. In the case of an NPI intensity increasing with the level of infection, it is possible to avoid the initial epidemic peak of great amplitude that would have occurred without intervention and to stabilize the epidemic at a chosen and sufficiently low endemic level. In the case of an NPI intensity decreasing with the level of infection, the epidemic can be driven to extinction by generating an "Allee" effect: when the incidence is below a given level, the epidemic goes extinct whereas, above it, the epidemic will still be able take hold at a lower endemic level. Simulations illustrate that appropriate NPIs could make the COVID-19 vanish relatively fast. We show that, in the context of the COVID-19 pandemic, most countries have not chosen to use the most efficient strategies. [ABSTRACT FROM AUTHOR]

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus. [ABSTRACT FROM AUTHOR]

(1) Background: The spread of agricultural green production technologies and systems among small farmers is affected by multiple factors such as subjectivity and objectivity. (2) Methods: Based on the marketability of agricultural green production socialization services (AGPSSs), this paper constructs a SEIRS model of infectious disease dynamics, taking the AGPSS of “MAP Sinochem Modern Agriculture” in Tianshan Town, Arhorchin Banner as an example. (3) Results: This study uses Python to simulate the process of forming a network of AGPSS for small farmers and analyzes the law of information dissemination among farmers. (4) Conclusions: This paper explores how multiple factors such as service quality, external environment, farmers’ willingness to decide, government guidance and the responsibility of service subjects play roles in the formation and diffusion of an AGPSS network so as to improve the quality and level of AGPSS provided by enterprises.

In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers. [ABSTRACT FROM AUTHOR]

In this paper we carry out a comparative study of an SEIRS model for vector borne diseases, taking awareness about the disease as a factor. The comparison is done using MATLAB. The susceptible human population is divided into aware and unaware susceptible population. Over a long period of time, aware susceptible population is more in dengue than in malaria. Also, the infected population is more in dengue than in malaria. Among the various control strategies used to control the population of the mosquitoes, the most efficient control measure is the treatment of infected humans by drugs. This treatment of drug is more effective in dengue than in malaria. [ABSTRACT FROM AUTHOR]

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings.

Each year infectious disease such as malaria causes severe population loss in both the developing and developed countries. Modeling of malaria is considered one of the effective ways to understand and mitigate this problem. This article develops a reliable quantitative modeling technique to support the design and characterization of the malaria disease in Bangladesh. Results reveal that the effects of some influencing factors such as service factors (i.e., lack of budgets in government agencies, antiviral medicine, and poor quality of service facilities), disease related factors (i.e., nutrition status and existing illness), environmental factors (i.e., urbanization and crowdedness), and sociological factors (i.e., education and religious believes) are significant. In particular, social factor education showed significant multidimensional impacts to the occurrence of the disease and its mitigation. A poor educational status leads to a range of impacts through (i) lack of awareness in the causes of malaria, severity of health effect and how and where to access the treatment services, (ii) refusal of vaccination, and (iii) unfamiliarity with good health and nutritional facts contributing to nutrition status. The study also provides the prediction of new cases in malaria until 2025 using the developed model and recommends, control strategies of malaria. [ABSTRACT FROM AUTHOR]

Abstract For an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the existence of global positive solutions. For sufficiently small values of the perturbation parameter, we prove the almost surely exponential stability of the disease-free equilibrium whenever a certain invariant R σ $\mathcal{R}_{\sigma}$ is below unity. Here R σ < R $\mathcal{R}_{\sigma}< \mathcal{R}$ , the latter being the basic reproduction number of the underlying deterministic model. Biologically, the main result has the following significance for a disease model that has an incubation phase of the pathogen: A small stochastic perturbation on the transmission rate from susceptible to infectious via the latent phase will enhance the stability of the disease-free state if both components of the perturbation are non-trivial; otherwise the stability will not be disturbed. Simulations illustrate the main stability theorem.

In this paper, we formulate an SEIRS model for the transmission of malaria as a system of non-linear ordinary differential equations. This model considers the human interaction coefficients as a constant as well as a function of the mosquito population. The equilibrium points were calculated and the local and global stability of the points were studied. The stability of the endemic equilibrium point has been shown using numerical simulation. Simulations were also performed by varying some parameters of the model. It was also found that the number of exposed and infected humans depended on the interaction coefficients. [ABSTRACT FROM AUTHOR]

Cultivated land protection is the top priority of the national economy in China and the livelihood of people. Cultivated land protection policies (CLPP) play an important role in the protection of cultivated land. However, the process of dissemination of CLPP on social networks of farmers has problems, such as distortion of policy content, single dissemination channels, low level of farmers’ knowledge, and low dissemination efficiency. For revealing the characteristics of the dissemination of CLPP in the farmers’ social networks (FSN), this study combines the Suspected–Exposed–Infected–Recovered–Suspected (SEIRS) epidemic model to construct a model of CLPP dissemination suitable for FSN. In addition, a numerical simulation of the dissemination process of CLPP is conducted on the FSN, and the influence of the structural characteristics of the FSN and different model parameters on the dissemination of CLPP is analyzed. Results show that (1) the dissemination rate between farmers in FSN has a significant impact on the scale and speed of CLPP. A greater initial dissemination rate corresponds to faster speed and larger scale of CLPP dissemination. (2) A greater node degree in FSN means stronger dissemination ability for CLPP. Therefore, identifying structural holes (opinion leaders) in FSN can effectively promote the dissemination of CLPP. (3) The SEIRS model can dynamically describe the evolution law of CLPP dissemination process over time through the four states of farmer nodes of suspected, exposed, infected, and recovered. Numerical simulation results show that the immune degradation rate is proportional to CLPP. However, the direct immunization rate is inversely proportional. The increase in immune degradation rate can reduce the number of recovered farmers and improve the efficiency of CLPP dissemination. On the basis of the abovementioned conclusions, this study draws policy recommendations to increase the scale and speed of CLPP dissemination in China.

This paper is concerned with the stability of an age-structured susceptible−exposed− infective−recovered−susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

For an SEIRS epidemic model with stochastic perturbations on transmission from the susceptible class to the latent and infectious classes, we prove the existence of global positive solutions. For sufficiently small values of the perturbation parameter, we prove the almost surely exponential stability of the disease-free equilibrium whenever a certain invariant $\mathcal{R}_{\sigma}$ is below unity. Here $\mathcal{R}_{\sigma}< \mathcal{R}$ , the latter being the basic reproduction number of the underlying deterministic model. Biologically, the main result has the following significance for a disease model that has an incubation phase of the pathogen: A small stochastic perturbation on the transmission rate from susceptible to infectious via the latent phase will enhance the stability of the disease-free state if both components of the perturbation are non-trivial; otherwise the stability will not be disturbed. Simulations illustrate the main stability theorem. [ABSTRACT FROM AUTHOR]

An SEIRS worm propagation model with two delays and vertical transmission in the network is investigated. It is proved that the positive equilibrium is locally asymptotically stable and the Hopf bifurcation can occur when the certain conditions are satisfied by regarding different combination of the two delays as bifurcation parameter. Then the properties of the Hopf bifurcation, such as direction and stability, are studied by using the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the obtained results and to demonstrate the dynamics of the model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, nonlinear incidence with a more general form and vertical transmission and the immunity period are considered in an SEIRS epidemic model. The basic reproductive number is obtained. If the basic reproductive number is smaller than one, the disease free equilibrium is asymptotically stable. When the basic reproductive number is bigger than one, regardless of the time delay length there exists a unique endemic equilibrium which is locally asymptotically stable under some conditions. By mathematical analysis and numerical simulations, the result shows that the immunity period and vertical transmission can influence the dynamic behaviors of the SEIRS system. To prolong the immunity period of the recovered and to reduce the part of vertical transmission by some measures are both favorable for controlling the disease. [Copyright &y& Elsevier]

Abstract: Moneim and Greenhalgh [I.A. Moneim, D. Greenhalgh, Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate, Math. Biosci. Eng. 2 (2005) 591–611] proposed an SEIRS epidemic model with general periodic vaccination strategy and seasonally varying contact rate. Their investigation shows that when , there exists a globally asymptotically stable disease-free periodic state, and when , the disease-free solution is unstable and there is at least one positive periodic solution. But they did not find the threshold condition for uniform persistence and extinction of the disease, and left a conjecture—that is, whether the basic reproduction ratio of the time-averaged system can be the threshold parameter or not. The present paper gives a negative answer to this question and provides a thorough global dynamics for this system. Numerical simulations which show our theoretical results are also given. [Copyright &y& Elsevier]

Abstract: This paper considers an SEIRS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle''s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficient conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations. [Copyright &y& Elsevier]

Human rabies, an infection of the nervous system, is a major public-health problem in China. In the last 60 years (1950-2010) there had been 124,255 reported human rabies cases, an average of 2,037 cases per year. However, the factors and mechanisms behind the persistence and prevalence of human rabies have not become well understood. The monthly data of human rabies cases reported by the Chinese Ministry of Health exhibits a periodic pattern on an annual base. The cases in the summer and autumn are significantly higher than in the spring and winter. Based on this observation, we propose a susceptible, exposed, infectious, and recovered (SEIRS) model with periodic transmission rates to investigate the seasonal rabies epidemics. We evaluate the basic reproduction number R, analyze the dynamical behavior of the model, and use the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health. We also carry out some sensitivity analysis of the basic reproduction number R in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R rather than the average basic reproduction number $\bar{R}_{0}$ or the basic reproduction number $\hat{R}_{0}$ of the corresponding autonomous system as a threshold for the disease. Finally, our studies show that human rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs, enhancing public education and awareness about rabies, and strengthening supervision of pupils and children in the summer and autumn. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number which is defined through the spectral radius of a linear integral operator. If , then the disease free periodic solution is globally asymptotically stable and if , then the disease persists. Our results really improve the results in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology Bull. Math. Biol. 69 (8) (2007) 2537–2559] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given. [Copyright &y& Elsevier]

Abstract: An epidemic transmission model SEIRS of malicious objects in the computer network is formulated, with death rate other than attack of malicious object is constant and an excess death rate constant for infective nodes. Deaths of a node in computer network equivalently mean to say the isolation of that node from the computer network which even on continuous run by anti malicious software spread malicious objects. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of standard form, namely proportional to I(t)/N(t), where N(t) is the total (variable) population size and I(t) is the size of infective population. The model consists of a set of integro-differential equations. When a node is recovered from the infected class, it recovers temporarily, acquiring temporary immunity with probability p (0⩽ p ⩽1) and dies from the attack of malicious object with probability (1− p). Malicious objects free equilibrium is investigated and the stability of the results are stated in terms of threshold parameter. [Copyright &y& Elsevier]

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Epidemiological models of COVID-19 transmission assume that recovered individuals have a fully protected immunity. To date, there is no definite answer about whether people who recover from COVID-19 can be reinfected with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In the absence of a clear answer about the risk of reinfection, it is instructive to consider the possible scenarios. To study the epidemiological dynamics with the possibility of reinfection, I use a Susceptible-Exposed-Infectious-Resistant-Susceptible model with the time-varying transmission rate. I consider three different ways of modeling reinfection. The crucial feature of this study is that I explore both the difference between the reinfection and no-reinfection scenarios and how the mitigation measures affect this difference. The principal results are the following. First, the dynamics of the reinfection and no-reinfection scenarios are indistinguishable before the infection peak. Second, the mitigation measures delay not only the infection peak, but also the moment when the difference between the reinfection and no-reinfection scenarios becomes prominent. These results are robust to various modeling assumptions., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier Ltd. All rights reserved.)