Dynamic Study of S1S2IR Waterborne Diseases Model Associated with the Consumption of Water Which Sources Change over a Year Following their Availability in a Semi-Arid Region of Cameroon

In the Sahelian zone of Cameroon, access to drinking water is a serious problem, and the type of drinking water used by the population is dynamic, changing according to its availability. We investigated an [Formula: see text] model of improved or unimproved water sources and waterborne disease infection in the city of Maroua, Cameroon. Statistical analysis of survey data, theoretical and numerical studies of this model was performed using MATLAB software. The basic reproduction number was derived to assess whether the infection would die out or persist. The equilibrium points of the model were found, and their stability was investigated. Our results showed that when [Formula: see text] the disease-free equilibrium is globally asymptotically stable, whereas when [Formula: see text], the disease-free equilibrium is unstable, and there exists a unique endemic equilibrium point that is globally asymptotically stable. Sensitivity analysis revealed that contamination parameters and changing water sources significantly influence the model. As shown in Figs. 4 , 7 , and 9 , extinction of waterborne diseases can occur when we maintain low parameter values ([Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], see Figs. 7 and 9 ); (([Formula: see text], [Formula: see text]), and ([Formula: see text], [Formula: see text]) see Figs. 4 (a) and 4 (b)); (([Formula: see text], [Formula: see text]) and ([Formula: see text], [Formula: see text]) see Figs. 4 (c) and 4 (d)). Numerical simulations suggest that maintaining low contamination rates and implementing hygienic measures can lead to the extinction of waterborne diseases. Public authorities must strictly enforce sanitary measures during the transition to a new main water source and ensure clean water quality for human consumption to prevent waterborne disease outbreaks.