In this paper, we analyzed dynamics of malaria disease by a compartment model involving ordinary differential equations for the human and mosquito populations. An equivalent system is obtained, which has two equilibriums: a disease-free equilibrium and an endemic equilibrium. The stability of these two equilibriums is controlled by the basic reproduction number . In this model the disease-free equilibrium state is stable if and if , the endemic equilibrium stable. The analytical predictions are conformed by numerical simulation and graphical results.
In the present paper, we proposed and analyzed an SIQR compartment model. Determine the steady state of the model and Stability analysis is carried out. Equilibrium analysis is presented and it is found that in each case the equilibrium Points are locally asymptotically stable under certain conditions The stability of the equilibriums are studied by using the Routh-Hurwitz criteria.
This paper examines an SIR epidemic model with a non-monotonic incidence rate. We analyzed the model by considering after infection, only a fraction of transmitted part is shifted to infectious and remaining part gets recovered without becoming infectious. We also analyze the dynamical behavior of the model and derive the stability conditions for the disease-free and the endemic equilibrium. We have found a threshold condition, in terms of basic reproduction number which is, less than one, the disease free equilibrium is globally attractive and if more than one, the endemic equilibrium exists and is globally stable. We illustrate theoretical results by carrying numerical simulation.
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