A Host-Vector SIR Model for Diarrhea Transmission: Analyzing the Role of Houseflies in Bangladesh

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.