Global stability analysis of a delayed susceptible-infected-susceptible epidemic model.
نویسندگان
چکیده
We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibrium is globally asymptotically stable. It is remarkable that the model dynamics is independent of the probability of immunity lost.
منابع مشابه
ON THE STABILITY AND THRESHOLD ANALYSIS OF AN EPIDEMIC MODEL
We consider a mathematical model of epidemic spread in which the population is partitioned into five compartments of susceptible S(t), Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t). We assume each of the compartments comprises of cohorts of individuals which are identical with respect to the disease status. We derive five systems of equations to represent each of the ...
متن کاملFuzzy Sliding Mode Controller Design and Analysis of an SQEIAR Epidemic Model for COVID-19 to Determine the Quarantine Rate
According to the global prevalence of coronavirus (COVID-19) pandemic, mathematical models can predict and control the dynamic behavior of the pandemic. Therefore, in this study, a comprehensive model is considered to examine the trend of COVID-19 based on Susceptible, Exposed, Infected (Symptomatic and Asymptomatic), and Recovered individuals. In the absence of a curative treatment or vaccinat...
متن کاملDynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...
متن کاملBifurcation Analysis on a Delayed Sis Epidemic Model with Stage Structure
In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic sol...
متن کاملStability and Numerical Analysis of Malaria- mTB- HIV/AIDS Co-infection (TECHNICAL NOTE)
In this paper, we develop a mathematical model to examine the transmission dynamics of curable malaria, curable mTB and non-curable HIV/AIDS and their co-infection. The size of population has been taken as varying due to the emigration of susceptible population. The total population is divided into five subclasses as susceptible, malaria infected, mTB infected, HIV infection and AIDS by assumin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of biological dynamics
دوره 9 Suppl 1 شماره
صفحات -
تاریخ انتشار 2015