Optimal Control of Shigellosis with Cost-Effective Strategies

In this paper, we apply optimal control theory to the model for shigellosis. It is assumed that education campaign, sanitation, and treatment are the main controls for this disease. The aim is to minimize the number of infections resulting from contact with careers, infectious population, and contaminated environments while keeping the cost of associated controls minimum. We achieve this aim through the application of Pontryagin's Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth-order Runge-Kutta schemes. We simulate the model under different strategies to investigate which option could yield the best results. The findings show that the strategy combining all three control efforts (treatment, sanitation, and education campaign) proves to be more beneficial in containing shigellosis than the rest. On the other hand, cost-effectiveness analysis is performed via incremental cost-effectiveness ratio (ICER). The findings from the ICER show that a strategy incorporating all three controls (treatment, sanitation, and education campaign) is the most cost-effective of all strategies considered in the study.