MATHEMATICAL ANALYSIS OF MULTICOMPARTMENT EPIDEMIC MODEL.

<p>In this paper, we study a nonlinear mathematical model in population with variable size. Size N(t) at time t, is divided into eight sub classes, with N(t) = S(t) + I(t) +I1(t)+I2(t)+I3(t)+I4(t)+ Q(t)+ R(t); where S(t), I(t), and Q(t) denote the sizes of the population susceptible to disease, and infectious members, 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 can be determined by the ratio called the basic reproductive number. This paper study the equilibrium, local stability and and the stochastic stability of the free disease equilibrium under certain conditions .