The conjecture of Arino and van den Driessche (2003) that a SIS type model in a moverstayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative or...

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also ...

In this paper, we analyze a mathematical model of tuberculosis (TB) epidemics for stability with respect to the basic reproduction number Ro. The basic reproduction number Ro is determined. We give criteria for stability of the disease – free equilibrium (DFE) and the endemic equilibrium

Based on the model provided by the Mulone and Straughan [1], we relax the population which are constant and obtain the drug-free equilibrium which is global asymptotically stable under some conditions. The system has only uniqueness positive endemic equilibrium which is globally asymptotically stable by using the second compound matrix.

The aim of this paper is to study the local stability of discrete epidemic models with specific nonlinear incidence rate. So, we establish criteria on local stability of the disease-free equilibrium, furthermore, using Schur-Cohn Criterion, important criterion on local stability of endemic equilibrium is also determined.

In this study, we modified continuous mathematical model for the dynamics of shigella outbreak at constant recruitment rate formulated by (Ojaswita et al., 2014). their model, they partitioned population into Susceptible (S), Infected (I) and recovered (R) individuals. We incorporated a vaccinated class (V), educated (G), exposed (E), asymptomatic (A) hospitalized (H) Bacteria (B) with correspo...

We analyze the impact of public health policy on spread a disease using version SIR model that includes vital statistics, waning immunity, and vaccination. This is rich enough to accommodate endemic steady states disease-free states. choose social distancing vaccines maximize an objective function penalizes lost output resulting from distancing, deaths disease, cost Surprisingly, even though eq...

An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction p of infectious immigrants is positive. If the basic reproduction number R0 is greater than 1, sufficient conditions for the global sta...

A deterministic compartmental model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The qualitatively analyzed to investigate its local asymptotic behavior respect disease-free and endemic equilibria. It shown, using Routh-Hurwitz criteria, that equilibrium locally asymptotically stable when associated basic reproduct...