Global and Local Stability of the Nonlinear Epidemic Model SIQS

In this paper, we studied the dynamics of SIQS a nonlinear epidemic model. The disease individ- uals will return to the susceptible class after a fixed period of time. The local stabilities and global stability of the infection -free equilibrium and endemic equilibrium are analyzed, respectively. Finally, we applied the Adomian decomposition method to the epidemiologic system, this method yields an analytical solution in terms of convergent infinite power series. The nonlinear epidemic model studies the transmission dynamics of infectious diseases witch assume that the size of the total population is constant. In this model we denotes the sizes of the population at time t, I and Q the sizes of the population susceptible to disease, infective members, and members who have been in quarantine with the possibility of infection, respectively. The stability of a disease-free status equilibrium and the existence of other nontrivial equilibrium can be determine by the ratio called the basic reproductive number, which quantifies the number of secondary infections arise from infected in a population. In the model presented here, we establish SIQS the nonlinear model that have members who have been in quaran- tine with the possibility of infection. We establish the global and local stability of the free-equilibrium and endemic respectively. Finally, we applied the Adomian decomposition method to the epidemiologic system. S (t) = (µ + γ − µ1 − β) S (t) + αI (t) − kS (t) I (t) + ν, ˙ I (t) = βS (t) − (µ2 + γ + α) I (t) + kS (t) I (t) + ρ, ˙ Q (t) = γI (t) − γS (t) − µ3Q (t) .