نوع مقاله : مقاله پژوهشی
نویسندگان
دانشکده علوم ریاضی، دانشگاه کاشان، کاشان، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
In this article, we present an $SIR$ model with a general nonlinear incidence rate, assuming a $100\%$ effective vaccine.
This system has a disease-free equilibrium point, corresponding to which a basic reproduction number $\mathscr{R}_0$ is obtained. For $\mathscr{R}_0 > 1$, the system will also have an endemic equilibrium point. We study the local and global stability of these equilibrium points. Considering the change in the stability status of the equilibrium points with the change of one of the parameters, we will examine the existence of a transcritical bifurcation. Additionally, we calculate the sensitivity index of $\mathscr{R}_0$, which essentially determines the susceptibility of the system to the existing parameters. Finally, we examine the obtained results with numerical examples.
کلیدواژهها [English]
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