Modeling the Impact of Treatment on Hepatitis B Burden: Mathematical Analysis and Simulation

Jean Pierre II Kouenkam (), Joseph Mbang (), Gilbert Chendjou (), Herieth Rwezaura () and Jean Tchuenche ()
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Jean Pierre II Kouenkam: Faculty of Science, University of Yaounde I
Joseph Mbang: University of Yaounde I
Gilbert Chendjou: University of Yaounde I
Herieth Rwezaura: University of Dar es Salaam
Jean Tchuenche: University of the Witwatersrand

SN Operations Research Forum, 2025, vol. 6, issue 4, 1-74

Abstract: Abstract Hepatitis B virus (HBV) infection represents a major public health threat, with high morbidity and mortality worldwide. Despite the availability of various drugs for its treatment, the disease still remains a significant global health concern. Chronic hepatitis B (CHB) is described in four phases, and among its long-term complications, cirrhosis and liver cancer cause a large burden. To investigate the impact of treatment on the disease burden, we formulate and analyze a new deterministic model as a system of nonlinear differential equations that includes these epidemiological characteristics of the disease, accounting for the classification of treated patients according to the phase of the disease. Theoretical analysis using standard dynamical systems approach exhibits a transcritical bifurcation. Thus, Hepatitis B (HB) can either be eradicated when the basic reproduction number $$\mathcal {R}_0 \le 1$$ R 0 ≤ 1 or persists otherwise. Simulation results to investigate the impact of treatment in Tokombere, a small village in the Far-North Region of Cameroon, show treatment has a high impact on reducing the incidences of compensated cirrhosis (CC), decompensated cirrhosis (DC), hepatocellular carcinoma (HCC), as well as mortality related to cirrhosis and HCC. Indeed, early detection and targeted treatment (ratio of 1 treated for 10 chronic carriers) of HBV carriers before the appearance of cirrhosis and carriers with CC before the onset of decompensation could potentially yield better outcomes in sub-Saharan Africa (SSA), where each step of the HBV continuum of care is severely affected by the lack of resources.

Keywords: Lyapunov methods; Compensated cirrhosis; Decompensated cirrhosis; Hepatocellular carcinoma; Sub-saharan Africa (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s43069-025-00567-1

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