Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control

Tahir Khan; Fathalla A. Rihan; Muhammad Ibrahim; Shuo Li; Atif M. Alamri; Salman A. AlQahtani; Tahir Khan; Fathalla A. Rihan; Muhammad Ibrahim; Shuo Li; Atif M. Alamri; Salman A. AlQahtani

doi:10.3934/mbe.2024230

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5207-5226. doi: 10.3934/mbe.2024230

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Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control

1.
Department of Mathematical Sciences, UAE University, P.O.Box 15551, Al-Ain, United Arab Emirates
2.
Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan
3.
School of Mathematics and Data Sciences, Changji University, Changji 831100, Xinjiang, China
4.
Software Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
5.
Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

Academic Editor: Yang Kuang

Received: 05 June 2023 Revised: 31 January 2024 Accepted: 01 February 2024 Published: 06 March 2024

Hepatitis B is one of the global health issues caused by the hepatitis B virus (HBV), producing 1.1 million deaths yearly. The acute and chronic phases of HBV are significant because worldwide, approximately 250 million people are infected by chronic hepatitis B. The chronic stage is a long-term, persistent infection that can cause liver damage and increase the risk of liver cancer. In the case of multiple phases of infection, a generalized saturated incidence rate model is more reasonable than a simply saturated incidence because it captures the complex dynamics of the different infection phases. In contrast, a simple saturated incidence rate model assumes a fixed shape for the incidence rate curve, which may not accurately reflect the dynamics of multiple infection phases. Considering HBV and its various phases, we constructed a model to present the dynamics and control strategies using the generalized saturated incidence. First, we proved that the model is well-posed. We then found the reproduction quantity and model equilibria to discuss the time dynamics of the model and investigate the conditions for stabilities. We also examined a control mechanism by introducing various controls to the model with the aim to increase the population of those recovered and minimize the infected people. We performed numerical experiments to check the biological significance and control implementation.
- epidemiological model,
- hepatitis B virus,
- multi-infection,
- generalize saturated incidence,
- stability and control analysis,
- numerical experiments
Citation: Tahir Khan, Fathalla A. Rihan, Muhammad Ibrahim, Shuo Li, Atif M. Alamri, Salman A. AlQahtani. Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5207-5226. doi: 10.3934/mbe.2024230

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Abstract

Hepatitis B is one of the global health issues caused by the hepatitis B virus (HBV), producing 1.1 million deaths yearly. The acute and chronic phases of HBV are significant because worldwide, approximately 250 million people are infected by chronic hepatitis B. The chronic stage is a long-term, persistent infection that can cause liver damage and increase the risk of liver cancer. In the case of multiple phases of infection, a generalized saturated incidence rate model is more reasonable than a simply saturated incidence because it captures the complex dynamics of the different infection phases. In contrast, a simple saturated incidence rate model assumes a fixed shape for the incidence rate curve, which may not accurately reflect the dynamics of multiple infection phases. Considering HBV and its various phases, we constructed a model to present the dynamics and control strategies using the generalized saturated incidence. First, we proved that the model is well-posed. We then found the reproduction quantity and model equilibria to discuss the time dynamics of the model and investigate the conditions for stabilities. We also examined a control mechanism by introducing various controls to the model with the aim to increase the population of those recovered and minimize the infected people. We performed numerical experiments to check the biological significance and control implementation.

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