Mathematical Model Analysis of Substance Abuse and Hepatitis B Co-Existence with Control Interventions

Substance abuse addictions and hepatitis B infections are two major public health problems facing humanity globally, especially in areas where the two problems co-exist. A mathematical model was used in this work to study the co-dynamics of substance abuse addictions and hepatitis B infections and investigate their possible control strategies. The mathematical features of the model, such as the disease-free equilibrium, endemic equilibrium, and basic reproduction number, were computed. The stability analysis of the disease-free equilibrium and endemic equilibrium was conducted analytically. The impact of multiple control measures, including public enlightenment, rehabilitation of individuals with substance abuse disorders, treatment of persons infected with hepatitis B, and vaccination of susceptible individuals, was examined numerically. The study reveals how co-existence fundamentally alters system behavior and control effectiveness and offers new insights for designing effective control management strategies.