Co-infection dynamics of two short term diseases with effect of recovery delay

Volume 29, Issue 4, pp 356--368 https://doi.org/10.22436/jmcs.029.04.05

Publication Date: November 24, 2022 Submission Date: March 24, 2022 Revision Date: June 13, 2022 Accteptance Date: July 21, 2022

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Authors

R. S. Tomar - ABV-Indian Institute of Information Technology and Management, Gwalior (MP), 474015, India. J. Dhar - ABV-Indian Institute of Information Technology and Management, Gwalior (MP), 474015, India. A. Kumar - ABV-Indian Institute of Information Technology and Management, Gwalior (MP), 474015, India.

Abstract

A co-infection model with two short-term diseases with delay in recovery is proposed. Here, we consider the simultaneous transmission of infection does not happen but of simultaneous recovery from both illnesses. The system consists of four epidemiological classes populations, namely: susceptible (\(S\)), an infected class with the first disease (\(I_1\)), an infected class with the second disease (\(I_2\)), co-infected class (\(I_{12}\)). We have found all possible equilibrium states, and the basic reproduction number also examined their stability without and with delay. Analytically, we have established that the local stability of equilibrium points depends on the basic reproduction number in the absence of recovery delay. But with delay, it requires some additional conditions. We have also checked the effect of delay on stability of endemic steady state numerically and showed that beyond a critical threshold value of delay parameter, the system loses its stability, and Hopf bifurcation occurs. Finally, a numerical simulation presented supports the analytical findings.

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Keywords

• Epidemic co-infection model
• recovery delay
• asymptotic stability
• Hopf-bifurcation

MSC

•  34A34
•  34C23
•  34C25
•  34D20
•  92D30

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