Mathematical analysis of an SIR respiratory infection model with sex and gender disparity: special reference to influenza A

Muntaser Safan; Muntaser Safan

doi:10.3934/mbe.2019131

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2613-2649. doi: 10.3934/mbe.2019131

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Research article

Mathematical analysis of an SIR respiratory infection model with sex and gender disparity: special reference to influenza A

Muntaser Safan ^{1,2
,
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1.
Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
2.
Department of Mathematical Sciences, Faculty of Applied Science, Umm Al-Qura University, 21955 Makkah, Saudi Arabia

Received: 11 November 2017 Accepted: 01 December 2018 Published: 26 March 2019

The aim of this work is to study the impact of sex and gender disparity on the overall dynamics of influenza A virus infection and to explore the direct and indirect effect of influenza A mass vaccination. To this end, a deterministic SIR model has been formulated and throughly analysed, where the equilibrium and stability analyses have been explored. The impact of sex disparity (i.e., disparity in susceptibility and in recovery rate between females and males) on the disease outcome (i.e., the basic reproduction number $R_0$ and the endemic prevalence of influenza in females and males) has been investigated. Mathematical and numerical analyses show that sex and gender disparities affect on the severity as well as the endemic prevalence of infection in both sexes. The analysis shows further that the efficacy of the vaccine for both sexes ($e_1 \& e_2$) and the response of the gender to mass-vaccination campaigns $\psi$ play a crucial role in influenza A containment and elimination process, where they impact significantly on the protection ratio as well as on the direct, indirect and total effect of vaccination on the burden of infection.
- SIR model,
- sex disparity,
- gender disparity,
- mass vaccination,
- local and global stability,
- controllability
Citation: Muntaser Safan. Mathematical analysis of an SIR respiratory infection model with sex and gender disparity: special reference to influenza A[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2613-2649. doi: 10.3934/mbe.2019131

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Abstract

The aim of this work is to study the impact of sex and gender disparity on the overall dynamics of influenza A virus infection and to explore the direct and indirect effect of influenza A mass vaccination. To this end, a deterministic SIR model has been formulated and throughly analysed, where the equilibrium and stability analyses have been explored. The impact of sex disparity (i.e., disparity in susceptibility and in recovery rate between females and males) on the disease outcome (i.e., the basic reproduction number $R_0$ and the endemic prevalence of influenza in females and males) has been investigated. Mathematical and numerical analyses show that sex and gender disparities affect on the severity as well as the endemic prevalence of infection in both sexes. The analysis shows further that the efficacy of the vaccine for both sexes ($e_1 \& e_2$) and the response of the gender to mass-vaccination campaigns $\psi$ play a crucial role in influenza A containment and elimination process, where they impact significantly on the protection ratio as well as on the direct, indirect and total effect of vaccination on the burden of infection.

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