Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the treatment control of infected population. We have analysed the exist...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 31; no. 1; pp. 53 - 67
Main Authors Ghosh, Jayanta Kumar, Ghosh, Uttam, Biswas, M. H. A., Sarkar, Susmita
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2023
Springer Nature B.V
Subjects
Computer Science
Disease control
Engineering
Mathematics
Mathematics and Statistics
Maximum principle
Optimal control
Original Research
Qualitative analysis
Stability analysis
Inhibitory factors
92D30
Transcritical bifurcation
34C23
37N25
Backward bifurcation
Optimal control
49J15
Efficiency analysis
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Summary:This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the treatment control of infected population. We have analysed the existence and stability of equilibrium points and investigated the transcritical and backward bifurcation. The Pontryagin’s maximum principle has been used to characterize the optimal control whose numerical results show the positive impact of two controls mentioned above for controlling the disease. Efficiency analysis is also done to determine the best control strategy among vaccination and treatment.
Bibliography:ObjectType-Article-1
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-019-00486-8