<p>In response to its rapid global spread, COVID-19 was designated a public health emergency of international concern by the World Health Organization (WHO) in early 2020. Since its emergence, the pandemic has been responsible for millions of deaths worldwide. Amid the widespread and disruptive progression of COVID-19, the management and treatment of several chronic diseases are deprioritized, with hepatitis B virus (HBV) being a notable example. The substantial surge in COVID-19 cases has led to a marked decline in the reporting and management of HBV infections, adversely affecting global efforts toward HBV elimination targets. Moreover, the presence of prior HBV with other viral agents raises serious concerns regarding HBV–COVID-19 coinfection, which may increase the disease burden and compromise treatment effectiveness. These factors collectively motivate the formulation of the present model. This paper proposes a novel mathematical model that extends the classical SIR model to describe the transmission dynamics of COVID-19 and HBV coinfection. The model incorporates distinct compartments to capture the progression of each infection and their interactions in coinfected individuals. Fundamental epidemiological properties, including nonnegativity and boundedness of solutions, are rigorously established. Using the next-generation matrix approach, the effective reproduction numbers of the model are derived. All equilibrium states, including the disease-free and endemic equilibria, are determined, and their stability properties are analyzed. The application of center manifold theory confirms that backward bifurcation does not occur in the model. A sensitivity analysis is conducted to assess the influence of key parameters on the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> through the normalized forward sensitivity index. In addition, the LHS–PRCC technique is employed to evaluate the impact of model parameters on population compartments. The HBV–COVID-19 coinfection model is further reformulated as an optimal control problem with two time-dependent control functions by applying Pontryagin’s maximum principle. The analysis focused on enhancing HBV treatment and increasing COVID-19 testing. Numerical simulations demonstrate that integrated intervention strategies that target both infections simultaneously are the most effective in reducing coinfection prevalence and overall disease burden. Overall, the model provides valuable insights into the transmission dynamics of HBV–COVID-19 coinfection and supports the design of effective intervention policies for managing the concurrent circulation of COVID-19 and HBV.</p>

Optimal control strategies for the transmission dynamics of HBV–COVID-19 coinfection: a nonlinear deterministic modeling approach

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发表日期：

2026年3月29日

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Md Hifzur Rahaman,
A. Karthik,
Mini Ghosh

摘要

In response to its rapid global spread, COVID-19 was designated a public health emergency of international concern by the World Health Organization (WHO) in early 2020. Since its emergence, the pandemic has been responsible for millions of deaths worldwide. Amid the widespread and disruptive progression of COVID-19, the management and treatment of several chronic diseases are deprioritized, with hepatitis B virus (HBV) being a notable example. The substantial surge in COVID-19 cases has led to a marked decline in the reporting and management of HBV infections, adversely affecting global efforts toward HBV elimination targets. Moreover, the presence of prior HBV with other viral agents raises serious concerns regarding HBV–COVID-19 coinfection, which may increase the disease burden and compromise treatment effectiveness. These factors collectively motivate the formulation of the present model. This paper proposes a novel mathematical model that extends the classical SIR model to describe the transmission dynamics of COVID-19 and HBV coinfection. The model incorporates distinct compartments to capture the progression of each infection and their interactions in coinfected individuals. Fundamental epidemiological properties, including nonnegativity and boundedness of solutions, are rigorously established. Using the next-generation matrix approach, the effective reproduction numbers of the model are derived. All equilibrium states, including the disease-free and endemic equilibria, are determined, and their stability properties are analyzed. The application of center manifold theory confirms that backward bifurcation does not occur in the model. A sensitivity analysis is conducted to assess the influence of key parameters on the basic reproduction number $R_0$ $R_{0}$ through the normalized forward sensitivity index. In addition, the LHS–PRCC technique is employed to evaluate the impact of model parameters on population compartments. The HBV–COVID-19 coinfection model is further reformulated as an optimal control problem with two time-dependent control functions by applying Pontryagin’s maximum principle. The analysis focused on enhancing HBV treatment and increasing COVID-19 testing. Numerical simulations demonstrate that integrated intervention strategies that target both infections simultaneously are the most effective in reducing coinfection prevalence and overall disease burden. Overall, the model provides valuable insights into the transmission dynamics of HBV–COVID-19 coinfection and supports the design of effective intervention policies for managing the concurrent circulation of COVID-19 and HBV.