Modeling Dynamics of Cholera a Perspective of Blood Groups, Treatment and Optimal Control

Abstract

Vibrio cholerae, an infectious bacterium prevalent in regions with limited access to safe water and sanitation facilities, is the causative agent of cholera, a highly transmissible disease. This study delves into the impact of medication and blood groupings on cholera dynamics through mathematical modeling. Various mathematical frameworks concerning cholera transmission have been previously proposed and examined. For instance, Faruque et al. (2006) explored how bacteriophages can mitigate cholera epidemics. Notably, individuals with blood type O are most susceptible to the disease, while those with blood type AB exhibit higher resistance. Investigating the influence of blood groups on cholera transmission patterns is a primary objective. Model analysis reveals that when the basic reproduction number exceeds unity, the disease-free equilibrium is asymptotically stable both locally and globally, while the endemic equilibrium is locally asymptotically stable. Three control strategies—disease prevention, therapy, and screening—are employed to address the optimal control problem. Cost-effectiveness analysis of these control measures suggests that a combined approach involving prevention, treatment, and screening is the most economical intervention strategy against the cholera pandemic. Numerical simulations conducted using MATLAB software illustrate the impact of blood type on cholera propagation, highlighting severe illness among individuals belonging to certain blood groups during outbreaks. Proper treatment of individuals with blood group O can significantly reduce mortality and the transmission rate of cholera.