Mathematical Analysis of Cryptosporidium Outbreak

Abstract

Cryptosporidium is a waterborne pathogen that transmits through various routes, including contact with the feces of infected individuals, contaminated environments, unsafe water, unsanitized food, raw or unpasteurized milk, animal exposure, and recreational water bodies. This study formulates and analyzes five compartmental models to propose effective strategies for controlling the spread of cryptosporidiosis. The models were assessed for biological and mathematical validity using the theory of positivity and were confirmed to be epidemiologically well-posed. The basic reproduction number was derived using the next generation matrix method and found to be less than unity, suggesting that the infection has the potential to be eliminated from the population. Stability analysis of the disease-free equilibrium was conducted using the Jacobian matrix method and confirmed local asymptotic stability. Sensitivity analysis identified the contact rate between susceptible and infected individuals as the most influential parameter affecting the basic reproduction number. This highlights the importance of reducing contact rates as a key intervention strategy. Numerical simulations performed using Maple 22 provided supportive insights and interpretations of the model dynamics, reinforcing the analytical findings.