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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Impact of Poverty on the Dynamic of Hepatitis B Spread

Journal of Vibration Testing and System Dynamics 9(4) (2025) 361--389 | DOI:10.5890/JVTSD.2025.12.005

Gallimard Nzinga Milongo$^{1}$, Apollinaire Ndondo Mboma$^{2,3}$, Martin Dountio$^{4}$, Franck Davhys Reval Langa$^{1}$

$^{1}$ Faculty of Sciences and Technics, Marien Ngouabi University, Brazzaville, Congo

$^{2}$ Faculty of Sciences, Department of Mathematical and Computer Science, University of Lubumbashi, DRC

$^3$ Faculty of Technological Sciences, Department of Basic Sciences New Horizons University, Lubumbashi, DRC

$^{4}$ Laboratory of Mathematics, Department of Mathematics and Computer Science, University of Douala, Cameroon

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Abstract

In this article, we develop and analyze a model that integrates both epidemic and economic aspects to assess the impact of poverty on the spread of hepatitis B. This model produces positive and bounded solutions. We demonstrate that the disease-free equilibrium is globally asymptotically stable when \(R_{0}^{h}<1\), while it becomes unstable when \(R_{0}^{h}>1\). Furthermore, we identify a unique endemic equilibrium. Additionally, we examine various investment cases using a critical value to evaluate how the factor of poverty influences populations infected with hepatitis B over a given period. The reduction in the disease can be attributed to increased capital, effective awareness programs, and improved healthcare coverage. To confirm these results, we conducted a sensitivity analysis using the PRCC method, which helps to understand the dynamics of hepatitis B and effectively guide public health efforts. Finally, we analyze the eradication and persistence of hepatitis B in the populations of developing countries, supported by numerical simulations. Our conclusions indicate that economic growth has a positive influence on the spread of hepatitis B.

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