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In this paper, we present and assess a predator–prey Leslie–Gower model including disease, refuge and treatment in prey population. There are two groups of prey: those who are susceptible and infected. It is hypothesized that prey population is affected by diseases and refuge, and grows logistically in the absence of predators. Infected prey population receives treatment. The predators’ growth rate is governed by the modified Leslie–Gower dynamics. The dynamical attributes of the resulting system are boundedness, positivity of solutions, extinction criteria, existence and (local and global) stability. Biology uses mathematical analysis to identify the possible attributes of equilibrium points. The focus of this study is to assess how treatment and refuge affect the populations of ill prey, susceptible prey, predators and treated prey. The numerical simulation indicates that the influence of treatment, and refuge change the dynamics of the system (2.1). Extensive numerical simulations were performed to validate our analytical findings by using the Mathematica and MATLAB software. [ABSTRACT FROM AUTHOR]

In this paper, SIR model with feedback control has been considered. By constructing the Lyapunov function, using the Routh–Hurwitz criterion and the positive definite quadratic form theory, some sufficient conditions have been obtained, and some well-known results have been generalized. It is worth mentioning that if the feedback control variables have an inhibitory effect on the susceptible population and the infected population, the number of basic regeneration of the disease will be reduced. The reduction depends only on the control of the susceptible population, but not on the control of the infected population. This is a very interesting conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we study an SSvEIQR model with nonlinear contact rate, isolation rate and vaccination rate driven by media coverage. First, the basic reproduction number R0 is derived. Then, the threshold dynamics of the disease are obtained in terms of R0: when R0 ≤ 1, the global stability of the disease-free equilibrium is obtained by constructing an appropriate Lyapunov function; when R0 > 1, the sufficient conditions to prove the globally stability of endemic equilibrium are obtained by applying the geometric method into the four-dimensional system, which needs to estimate the Lozinskiǐ measure of a 6 × 6 matrix. Further, we conduct some numerical simulations to validate our theoretical results, and analyze the impact of media coverage on disease transmission, the results show that media coverage could effectively suppress the spread of the disease and reduce the number of infected individuals. Finally, through the sensitivity analysis of R0, we obtain some measures to control the spread of the disease, such as reducing contact, strengthening isolation and vaccination. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Zika transmission model which considers human-to-human sexual transmission, the extrinsic incubation period of mosquitoes, and the vector-bias effect. Firstly, the explicit expression of the basic reproduction number R0 is given by using the next-generation operator method, and the global dynamics of the model are established by taking R0 as the threshold condition, that is, if R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, if R0 > 1, the model has a unique endemic equilibrium that is locally asymptotically stable and the disease persists. And when we ignore the vector-bias effect, the global asymptotic stability of the endemic equilibrium is proved by constructing a Lyapunov function. Then, we select the reported epidemic data from Brazil for fitting, which verifies the obtained theoretical results. Meanwhile, we study the impact of human-to-human sexual transmission rate and mosquito-to-human transmission rate on the spread and prevalence of Zika. In addition, we calculate the sensitivity indices of R0 to the model parameters and provide effective measures to control Zika transmission. The simulation results indicate that extending the extrinsic incubation period of mosquitoes is beneficial for disease control while ignoring the vector-bias effect will underestimate the risk of Zika transmission. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model. By incorporating the Crowley–Martin type functional response and a saturated treatment function, the model effectively captures the intricacies of real-world epidemics. Our research establishes the existence, uniqueness, non-negativity and boundedness of the solution, while also investigating the model’s fundamental reproduction number. Additionally, we conduct a thorough analysis of the specific conditions governing the local and global stability of the model’s equilibriums. A notable observation is the variation of the reproduction number with the fractional-order α, which represents a memory effect on individuals’ dynamic behavior and reveals the influence of interactions between compartments. To validate these theoretical findings, we employ numerical simulations using Matlab, demonstrating that inhibition measures for susceptibles and the saturated treatment parameters play a pivotal role in determining the disease state. Specifically, we observe that as these parameter values increase, the transition from endemic equilibrium to disease-free equilibrium occurs. [ABSTRACT FROM AUTHOR]

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus (SEIRV) model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission. The Lyapunov function using Volterra–Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point. An optimal control strategy is proposed to prevent the spread of coronavirus, in addition to governmental intervention. The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment. A numerical study of the model is also carried out to investigate the analytical results. [ABSTRACT FROM AUTHOR]