In this work, we consider a nonlinear epidemic model with temporary immunity and a saturated incidence rate. N (t) at time t, this population is divide into eight sub-classes, with N(t) = S(t) + I(t) +I1(t)+I2(t)+O(t)+A(t)+ Q1(t)+ Q2(t). S(t), I(t), I1(t), I2(t), O(t), A(t), Q1(t) and Q2(t), denote the sizes of the population susceptible to disease, infectious members, HIV infected members that do not know they are infected, HIV members that know they are infected, members suffering from other opportunistic infections, AIDS members, and quarantine members. With the possibility of infection through temporary immunity, respectively. The stability of a disease-free status equilibrium and the existence of endemic equilibrium determined by the ratio called the basic reproductive number. The model has been studied the permanence of the epidemic and Stochastic stability of the free disease equilibrium under certain conditions.
Basic reproduction number, endemic equilibrium, epidemic model stability, stochastic stability, saturated incidence
Cite this paper
Laid Chahrazed. (2020) Stochastic Stability and Permanence for Delay of an Epidemic Model with Incidence Rate. International Journal of Biology and Biomedicine, 4, 11-15