Diarrhea is responsible for killing around 525,000 children every year, even though it is preventable and treatable. More than 130 nations are affected by the illness of diarrhea. Mathematical models provide a valuable tool for understanding the dynamics of infectious diseases like diarrhea and evaluating potential control strategies. To understand its transmission dynamics in Bangladesh, this study develops a Susceptible-Infectious-Recovered (SIR) mathematical model that incorporates both the human (host) and housefly (vector) populations. The model consists of five nonlinear ordinary differential equations (ODEs). We analyze the model to determine its equilibrium points and the basic reproduction number (R₀ ). Using demographic and epidemiological parameters for Jashore and Khulna, Bangladesh, we calculate the basic reproduction number to be R₀=1.35. This value, being greater than 1, indicates that the disease-free state is unstable and predicts a stable endemic equilibrium where diarrhea persists in the population. Numerical simulations for Khulna and Jashore illustrate this endemic dynamic, showing a decline in initial infections followed by long-term persistence. The findings confirm the model's utility in explaining the endemic nature of diarrhea in the region and highlight that interventions targeting vector (housefly) control are essential for effective public health strategies.

People around the world use fresh water daily for drinking, sanitation, and washing. At the same time, they discharge wastewater into canals, which can be harmful to both human health and the ecosystem of surface water sources. A significant amount of water is consumed for washing purposes. However, it is possible to disinfect and purify this large volume of wastewater for reuse. The process of treating used wastewater is known as refinement. This study aims to develop a two-stage stochastic recourse model that refines wastewater before it is released into the environment. The goal is to ensure that the refined wastewater does not harm the ecosystem. The treated water can then be repurposed for various secondary uses. The proposed model will account for uncertainties related to the availability of water from the supplying authority. To evaluate the effectiveness of this model, we will compare the costs of the water supply system both with and without refinement. The advantages of the proposed model will be assessed through calculations of the expected value of perfect information (EVPI), the value of the stochastic solution (VSS), the recourse solution (RS), the wait-and-see solution (WS), and the expected solution based on first-stage decisions (EEV). Additionally, a risk-averse (RA) optimization model will be used to analyze the sensitivity of system costs.