background and aims: the world is threatened by disease outbreak that reaches a public health emergency of international concern, studies to inform public and agencies for effective containment strategy are necessary. several studies provided vital information of the dynamics and control of ebola epidemic outbreak in west africa. methodologies and techniques in those researches have to be revie...

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf...

The main purpose of this paper is to explore the dynamics of an epidemic model with a general nonlinear incidence βSI/(1 + αI). The existence and stability of multiple endemic equilibria of the epidemic model are analyzed. Local bifurcation theory is applied to explore the rich dynamical behavior of the model. Normal forms of the model are derived for different types of bifurcations, including ...

We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on the networks. We analytically demonstrate that, in the case when the recovery time τR is larger than the infection time τI , the infection flows on a one direction, i. e. from an infected node to its susceptible neighbor bu...

in this paper, a five–dimensional mathematical model is proposed for the transmission dynamics of hiv/aids within a population of varying size. in writing the model, we have divided the population under consideration into five sub classes of susceptible, infective, pre-aids, aids related complex and that of aids patients. the model has two non- negative equilibria namely, a disease free and the...

Estimation of the domain of attraction of a class of susceptible infectious removed susceptible (SIRS) epidemic models for varying-size population with constant immigration is investigated. On assumption that the disease-free equilibrium and the endemic equilibrium exist, the domain of attraction of epidemic model is estimated by using sum-of-squares optimization approach. An invariant subset o...