Optimal control strategies for water, sanitation, and hygiene in mitigating spread of waterborne diseases

Improving access to water, sanitation and hygiene (WASH) can help to eliminate the root cause of waterborne disease transmission. WASH has the potential to function as a sustained and effective mechanism for controlling enteric diarrheal disease (EDD) over the long term. To address this question, we formulate a mathematical model to study the impact of WASH services on reducing the transmission of waterborne diseases. The model is analyzed using the stability theory of differential equations in order to determine the threshold condition in disease control. We utilize optimal control theory to find the right balance in WASH interventions, ensuring a decrease in waterborne disease over a specific planning period. The total number of EDD cases is minimized when there are specific financial restrictions. To analyze the outcomes, we employed numerical simulations and conducted a sensitivity analysis on different weights in the cost index. Furthermore, we compared the numerical simulations of the optimal solutions and performed multiple regression analyses to gain insights into the impact of control strategies. Our findings reveal that wastewater and sewage treatment (WST) control has the most significant impact. When multiple controls are necessary, WST and drinking water supply (DWS) control provide the most effective combination. These results have significant implications for controlling infectious diseases, especially in developing countries where budgets are typically limited. Implementing these strategies could potentially reduce disease transmission and improve public health outcomes.