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.
Kazemi, R. and Shakeri, M. A. (2024). Analysis of an $SIR$ Model with Nonlinear Incidence Rate and the Full Impact of Vaccination. Journal of Advanced Mathematical Modeling, 14(2), 96-108. doi: 10.22055/jamm.2024.47445.2290
MLA
Kazemi, R. , and Shakeri, M. A. . "Analysis of an $SIR$ Model with Nonlinear Incidence Rate and the Full Impact of Vaccination", Journal of Advanced Mathematical Modeling, 14, 2, 2024, 96-108. doi: 10.22055/jamm.2024.47445.2290
HARVARD
Kazemi, R., Shakeri, M. A. (2024). 'Analysis of an $SIR$ Model with Nonlinear Incidence Rate and the Full Impact of Vaccination', Journal of Advanced Mathematical Modeling, 14(2), pp. 96-108. doi: 10.22055/jamm.2024.47445.2290
CHICAGO
R. Kazemi and M. A. Shakeri, "Analysis of an $SIR$ Model with Nonlinear Incidence Rate and the Full Impact of Vaccination," Journal of Advanced Mathematical Modeling, 14 2 (2024): 96-108, doi: 10.22055/jamm.2024.47445.2290
VANCOUVER
Kazemi, R., Shakeri, M. A. Analysis of an $SIR$ Model with Nonlinear Incidence Rate and the Full Impact of Vaccination. Journal of Advanced Mathematical Modeling, 2024; 14(2): 96-108. doi: 10.22055/jamm.2024.47445.2290
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