We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the...

In this paper, we derive and study the classical SIR, SIS, SEIR and SEI models of epidemiological dynamics with time delays and a general incidence rate. By constructing Lyapunov functionals, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is shown. This analysis extends and develops further our previous results and can be applied to the other biologi...

We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number R0. We present that when R0 ≤ 1, there is a unique disease-free equilibrium which is globally asymptotically stable; when R0 > 1, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the...

The spread of tuberculosis is studied through two models which include fast and slow progression to the infected class. For each model, Lyapunov functions are used to show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is globally asymptoti...

An SIS/SAS model of gonorrhea transmission in a men-seeking-men (MSM) system is presented in this paper to study the impact of education on the dynamics of gonorrhea prevalence. Education affects behaviors that may fall into two categories– prevention and disease status awareness. Stability conditions for the disease free equilibrium and endemic equilibrium are determined along with an analytic...

Abstract. In this paper, we study a class of multi-group SIRS epidemic models with nonlinear incidence rate which have cross patch infection between different groups. The basic reproduction number R0 is calculated. By using the method of Lyapunov functions, LaSalle’s invariance principle, the theory of the nonnegative matrices and the theory of the persistence of dynamical systems, it is proved...

It has long been known that there is a relation between boundary sineGordon theory and thermodynamics of charge neutral two-component Coulomb plasma on a unit circle. On the other hand, recently it was found that open string worldsheet description of brane decay can be related to a sequence of points of thermodynamic equilibrium of one-component plasma. Here we consider a different decay proces...

A delayed SIR epidemic model with a generalized incidence rate is studied. The time delay represents the incubation period. The threshold parameter, R0(τ) is obtained which determines whether the disease is extinct or not. Throughout the paper, we mainly use the technique of Lyapunov functional to establish the global stability of both the disease-free and endemic equilibrium.

In this paper, we study a stochastic SIS epidemic model with distributed delays. The positiveness of the solutions is established. We obtain sufficient conditions for extinction disease through stability disease-free equilibrium and same in mean. Compared to many works on deterministic models their stability, delays involved offer new much more boundedness rate losing immunity. extinct small la...

The Corona virus is a disease that threatens human population on earth in early 2020, the first infection began China, thought to be host mammals and then able transmits into body, this present paper will describe dynamic system of Covid-19, analyzing direction equilibrium, Disease Free Equilibrium (DFE) Endemic (EE), which can done by determining dimensionless number Basic Reproduction Number ...