A Cost-Effective Epidemiological Exposition of Diphtheria Outbreak by the Optimal Control Model: A Case Study of Rohingya Refugee Camp in Bangladesh

We consider a deterministic optimal control approach with cost-effectiveness analysis for the diphtheria outbreak in the Rohingya refugee camp in Bangladesh. A deterministic epidemic dynamical model for diphtheria outbreaks has been developed with three optimal controls: vaccination, latent, and infectious treatment. Here, the qualitative study of the model has been interpreted. An objective function has been regarded as a cost function introduced by the optimal controls and the diseases themselves. Then, the existence and uniqueness of the optimal system have also been shown with the help of Pontryagin’s minimum principle. A numerical investigation has been carried out to solve the state and adjoint systems of optimality conditions. Furthermore, it has been investigated using several levels of availability of the optimal controls (vaccination, latent, and infectious treatment) to identify which level gives the best outcomes. Moreover, the cost-effective analysis has been inquired with the numerical value of the cost function and the total cured population in each control strategy to clarify the strategy with the least cost but maximum remediation.