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Volume 7, Issue 3
Optimal and Stability Analysis of the Co-Infections Disease Mathematical Model

Zhila Siosemardan, Nemat Nyamoradi, S. Hariharan & L. Shangerganesh

DOI: 10.12150/jnma.2025.840

J. Nonl. Mod. Anal., 7 (2025), pp. 840-867.

Published online: 2025-05

[An open-access article; the PDF is free to any online user.]

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  • Abstract

A co-infection of a human or a pig with human influenza or COVID-19 strains and H5N1 strain may result in a pandemic strain, causing a widespread deadly pandemic. In this paper, we consider a new class of co-infections disease epidemic models for a rapid and slow virus. We study the transmission threshold by analyzing the basic reproduction number. The equilibrium points for the model are derived, and their local stability is analyzed with suitable assumptions on the model parameters. Understanding the model parameters is one of the prime subjects in this research work. Therefore, the sensitivity of essential parameters is investigated. Moreover, the optimal control problem for the proposed model is considered, and first-order optimality conditions are derived. Finally, numerical simulations indicate the effects of the model’s basic reproduction number and control variables.

  • Keywords

Co-infections model, stability analysis, basic reproduction number, optimal control.

  • AMS Subject Headings

34D05, 34D20, 49J15, 92C60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-840, author = {Siosemardan , ZhilaNyamoradi , NematHariharan , S. and Shangerganesh , L.}, title = {Optimal and Stability Analysis of the Co-Infections Disease Mathematical Model}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {3}, pages = {840--867}, abstract = {

A co-infection of a human or a pig with human influenza or COVID-19 strains and H5N1 strain may result in a pandemic strain, causing a widespread deadly pandemic. In this paper, we consider a new class of co-infections disease epidemic models for a rapid and slow virus. We study the transmission threshold by analyzing the basic reproduction number. The equilibrium points for the model are derived, and their local stability is analyzed with suitable assumptions on the model parameters. Understanding the model parameters is one of the prime subjects in this research work. Therefore, the sensitivity of essential parameters is investigated. Moreover, the optimal control problem for the proposed model is considered, and first-order optimality conditions are derived. Finally, numerical simulations indicate the effects of the model’s basic reproduction number and control variables.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.840}, url = {http://global-sci.org/intro/article_detail/jnma/24105.html} }
TY - JOUR T1 - Optimal and Stability Analysis of the Co-Infections Disease Mathematical Model AU - Siosemardan , Zhila AU - Nyamoradi , Nemat AU - Hariharan , S. AU - Shangerganesh , L. JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 840 EP - 867 PY - 2025 DA - 2025/05 SN - 7 DO - http://doi.org/10.12150/jnma.2025.840 UR - https://global-sci.org/intro/article_detail/jnma/24105.html KW - Co-infections model, stability analysis, basic reproduction number, optimal control. AB -

A co-infection of a human or a pig with human influenza or COVID-19 strains and H5N1 strain may result in a pandemic strain, causing a widespread deadly pandemic. In this paper, we consider a new class of co-infections disease epidemic models for a rapid and slow virus. We study the transmission threshold by analyzing the basic reproduction number. The equilibrium points for the model are derived, and their local stability is analyzed with suitable assumptions on the model parameters. Understanding the model parameters is one of the prime subjects in this research work. Therefore, the sensitivity of essential parameters is investigated. Moreover, the optimal control problem for the proposed model is considered, and first-order optimality conditions are derived. Finally, numerical simulations indicate the effects of the model’s basic reproduction number and control variables.

Siosemardan , ZhilaNyamoradi , NematHariharan , S. and Shangerganesh , L.. (2025). Optimal and Stability Analysis of the Co-Infections Disease Mathematical Model. Journal of Nonlinear Modeling and Analysis. 7 (3). 840-867. doi:10.12150/jnma.2025.840
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