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SEIR Mathematical Model for Influenza-Corona Co-Infection with Treatment and Hospitalization Compartments and Optimal Control Strategies

by Muhammad Imran1,*, Brett McKinney1, Azhar Iqbal Kashif Butt2

1 Tandy School of Computer Science, University of Tulsa, Tulsa, OK 74104, USA
2 Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, 31982, Saudi Arabia

* Corresponding Author: Muhammad Imran. Email: email

(This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)

Computer Modeling in Engineering & Sciences 2025, 142(2), 1899-1931. https://doi.org/10.32604/cmes.2024.059552

Abstract

The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms. This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR (Susceptible-Exposed-Infectious-Recovered) framework to incorporate treatment and hospitalization compartments. The population is divided into eight compartments, with infectious individuals further categorized into influenza infectious, corona infectious, and co-infection cases. The proposed mathematical model is constrained to adhere to fundamental epidemiological properties, such as non-negativity and boundedness within a feasible region. Additionally, the model is demonstrated to be well-posed with a unique solution. Equilibrium points, including the disease-free and endemic equilibria, are identified, and various properties related to these equilibrium points, such as the basic reproduction number, are determined. Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number. Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity. Furthermore, an optimal control problem is defined to minimize disease transmission and to control strategy costs. The purpose of our study is to identify the most effective (optimal) control strategies for mitigating the spread of the co-infection with minimum cost of the controls. The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health. This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection, helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.

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APA Style
Imran, M., McKinney, B., Butt, A.I.K. (2025). SEIR mathematical model for influenza-corona co-infection with treatment and hospitalization compartments and optimal control strategies. Computer Modeling in Engineering & Sciences, 142(2), 1899–1931. https://doi.org/10.32604/cmes.2024.059552
Vancouver Style
Imran M, McKinney B, Butt AIK. SEIR mathematical model for influenza-corona co-infection with treatment and hospitalization compartments and optimal control strategies. Comput Model Eng Sci. 2025;142(2):1899–1931. https://doi.org/10.32604/cmes.2024.059552
IEEE Style
M. Imran, B. McKinney, and A. I. K. Butt, “SEIR Mathematical Model for Influenza-Corona Co-Infection with Treatment and Hospitalization Compartments and Optimal Control Strategies,” Comput. Model. Eng. Sci., vol. 142, no. 2, pp. 1899–1931, 2025. https://doi.org/10.32604/cmes.2024.059552



cc Copyright © 2025 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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