Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
|Number of page(s)
|22 March 2021
Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment
Boalia Junior High School,
West Bengal, India.
2 Department of Applied Mathematics, University of Calcutta, Kolkata, India.
* Corresponding author: uttam email@example.com
Accepted: 6 January 2021
This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point (DFE) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov-Takens bifurcation (BT) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.
Mathematics Subject Classification: 37N25 / 34C23 / 49J15 / 92D30
Key words: Logistic growth / non-monotonic incidence / non-hyperbolic equilibrium point / transcritical bifurcation / backward bifurcation / Bogdanov-Takens bifurcation / optimal control / efficiency analysis
© The authors. Published by EDP Sciences, 2021
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