Stochastic modeling and analysis of Hepatitis and Tuberculosis co-infection dynamics

Abstract Several mathematical models have been developed to investigate the dynamics of Tuberculosis (TB) and Hepatitis B virus (HBV). Numerous current models for TB, HBV, and their co-dynamics fall short in capturing the important and practical aspect of unpredictability. It is crucial to take into account a stochastic co-infection HBV–TB epidemic model since different random elements have a substantial impact on the overall dynamics of these diseases. We provide a novel stochastic co-model for TB and HBV in this study, and we establish criteria on the uniqueness and existence of a non-negative global solution. We also looked at the persistence of the infections as long its dynamics are governable by the proposed model. To verify the theoretical conclusions, numerical simulations are presented keeping in view the associated analytical results. The infections are found to finally die out and go extinct with certainty when Lévy intensities surpass the specified thresholds and the related stochastic thresholds fall below unity. The findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given population. Our results provide insights into effective intervention strategies, ultimately aiming to improve the management and control of TB and HBV co-infections.