Modeling Tuberculosis Transmission and Control Using Game Theory and Optimal Strategies Incorporating Migration Flow Dynamics - Md. Abu Salek; Mehmet Yavuz; Md. Humayun Kabir; Jannatun Nayeem; Muhammad Hossain; Md. Fayz-Al-Asad (Jambura Journal of Biomathematics (JJBM), 2026)
A Tuberculosis (TB) transmission model,which optimizes the control strategy with migration dynamics utilizing evolutionary game theory, has been introduced in this work. Besides, the population dynamics is categorized into susceptible, vaccinated, migratory, exposed, infectious, treated, and recovered individuals, while three dynamic controls,distancing, vaccination, and treatment,modulate the spread of disease. Each control measure is considered within the range of 0 to 1 for the governing parameters,namely, migration rate ($λ$), treatment rate ($γ$), recovery rate ($δ$) and transmission rate ($β$).This study develops a migration-integrated tuberculosis transmission model incorporating susceptible, vaccinated, migratory, exposed, infectious, treated, and recovered populations. Three intervention strategies, namely distancing, vaccination, and treatment, are included to examine their effects on TB transmission. The basic reproduction number is derived, and the positivity and boundedness of the model are established. Numerical simulations are performed using an Adams–Bashforth–Moulton predictor–corrector method. A formal evolutionary game-theoretic framework is introduced through payoff functions and replicator dynamics to evaluate the behavioral preference among the control strategies. The results indicate that treatment produces the strongest reduction in infection prevalence when applied as a single control, while combined strategies provide stronger epidemic suppression when sufficient resources are available. Cost-effectiveness analysis is used to compare the economic efficiency of the intervention strategies. The findings highlight the importance of incorporating migration and behavioral responses into tuberculosis control planning.