OPTIMAL CONTROL STRATEGY ON MATHEMATICAL MODELING OF SYPHILIS INFECTION

In this thesis, our study focused on developing a mathematical model for the Syphilis disease, incorporating optimal control strategies. Initially, we rigorously established the positivity and boundedness of the model’s solution within a specified domain. Moreover, utilizing the next generation matrix, we derived a basic reproduction number, which is crucial for assessing disease dynamics. Both local and global stability of the disease-free equilibrium and endemic equilibrium point of the model equation was established. The results show that, if the basic reproduction number is less than one, the solution converges to the disease-free steady-state, rendering the disease-free equilibrium asymptotically stable. To assess their impact on disease transmission dynamics, we conducted sensitivity analysis of the model equation on the key parameters. We extended the model to optimal control by incorporate control measures, such as preventive interventions for protecting susceptible individuals and treatment strategies for reducing infectious transmission, was obtained through the Pontryagin minimum principle. The efficacy of the proposed models was validated through numerical simulations, and sensitivity analysis provided valuable insights into their robustness. Our analysis suggests that integrating available treatment and prevention techniques to mitigate Syphilis outbreaks yields greater efficacy. Ultimately, numerical simulations emphasize that the most optimal approach involves a synergistic application of prevention and treatment strategies to minimize disease burden.