An SIS sex-structured influenza A model with positive case fatality in an open population with varying size

Muntaser Safan; Bayan Humadi; Muntaser Safan; Bayan Humadi

doi:10.3934/mbe.2024306

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 8: 6975-7011. doi: 10.3934/mbe.2024306

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Research article

An SIS sex-structured influenza A model with positive case fatality in an open population with varying size

Muntaser Safan ^{1,2
,
,},
Bayan Humadi ¹

1.
Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, KSA
2.
Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Academic Editor: Yang Kuang

Received: 17 May 2024 Revised: 20 July 2024 Accepted: 09 August 2024 Published: 27 August 2024

This work aims to study the role of sex disparities on the overall outcome of influenza A disease. Therefore, the classical Susceptible-Infected-Susceptible (SIS) endemic model was extended to include the impact of sex disparities on the overall dynamics of influenza A infection which spreads in an open population with a varying size, and took the potential lethality of the infection. The model was mathematically analyzed, where the equilibrium and bifurcation analyses were established. The model was shown to undergo a backward bifurcation at $ \mathcal{R}_0 = 1 $, for certain range of the model parameters, where $ \mathcal{R}_0 $ is the basic reproduction number of the model. The asymptotic stability of the equilibria was numerically investigated, and the effective threshold was determined. The differences in susceptibility, transmissibility and case fatality (of females with respect to males) are shown to remarkably affect the disease outcomes. Simulations were performed to illustrate the theoretical results.
- SIS model,
- equilibria,
- case fatality,
- backward bifurcation,
- effective threshold,
- sex and gender disparities,
- influenza A
Citation: Muntaser Safan, Bayan Humadi. An SIS sex-structured influenza A model with positive case fatality in an open population with varying size[J]. Mathematical Biosciences and Engineering, 2024, 21(8): 6975-7011. doi: 10.3934/mbe.2024306

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Abstract

This work aims to study the role of sex disparities on the overall outcome of influenza A disease. Therefore, the classical Susceptible-Infected-Susceptible (SIS) endemic model was extended to include the impact of sex disparities on the overall dynamics of influenza A infection which spreads in an open population with a varying size, and took the potential lethality of the infection. The model was mathematically analyzed, where the equilibrium and bifurcation analyses were established. The model was shown to undergo a backward bifurcation at $ \mathcal{R}_0 = 1 $, for certain range of the model parameters, where $ \mathcal{R}_0 $ is the basic reproduction number of the model. The asymptotic stability of the equilibria was numerically investigated, and the effective threshold was determined. The differences in susceptibility, transmissibility and case fatality (of females with respect to males) are shown to remarkably affect the disease outcomes. Simulations were performed to illustrate the theoretical results.

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