In this paper, an SIR epidemic model with nonlinear incidence rate and double delays due to the force of infection and temporary immunity period is investigated. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition R0, the basic reproduction number. Based on some comparison arguments, sharp threshold conditions which are necessary for the...

We formulate a model to describe the dynamics of hepatitis C virus (HCV) considering four populations: uninfected liver cells, infected liver cells, HCV and T cells. Analysis of the model reveals the existence of two equilibrium states, the uninfected state in which no virus is present and an endemically infected state, in which virus and infected cells are present. There exists a threshold con...

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...

In this paper, a fractional-order model for the spread of computer viruses with saturated treatment rate is presented. This model consists of three components: Susceptible, Infectious, and Recovered. The SIR epidemic model with saturated treatment rate is considered. The stability of the disease free and endemic equilibrium points are studied. The global stability of the disease free equilibriu...

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...

*Correspondence: [email protected] School of Mathematics and Computer Science, Shanxi Normal University, Linfen, P.R. China Abstract In this paper, we study a new SEIRS epidemic model describing nonlinear incidence with a more general form and the transmission of influenza virus with disease resistance. The basic reproductive number 0 is obtained by using the method of next generating matrix. ...

We extend a recent investigation by Meehan et al. (2017) [1] regarding the global stability properties of the general Kermack-McKendrick model to the multi-strain case. We demonstrate that the basic reproduction number of each strain R0j represents a sharp threshold parameter such that when R0j ≤ 1 for all j each strain dies out and the infection-free equilibrium is globally asymptotically stab...

We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential inf...

Abstract: In this paper, a delayed ratio-dependent eco-epidemiological model with Holling type III functional response and two time delays is investigated.By regarding the delay as the bifurcation parameter, local stability of each equilibrium is discussed at the endemic equilibrium. By analyzing the corresponding characteristic equations, the conditions for existence of Hopf bifurcation for th...

Radicalization is the process by which people come to adopt increasingly extreme political, social or religious ideologies. When radicalization leads to violence, radical thinking becomes a threat to national security. De-radicalization programs are part of an effort to combat violent extremism and terrorism. This type of initiatives attempt to alter violent extremists radical beliefs and viole...