Modeling and controlling Leptospirosis transmission in humans and rodents

Leptospirosis is a commonly undiagnosed and under-reported bacterial disease that affects both animals and humans. Studies suggest that the risk of infection varies based on individuals' occupations and living environments. This study employs a mathematical model that assesses the impact of rodent-borne diseases on human populations. A disease-causing agent in the environment can lead to human infection. Additionally, humans can become infected by interacting with infected rodents. The purpose of this paper is to construct a SIR (human)-SI (rodent) model of bacterial populations with Holling type II functional responses, as well as chemical disinfectants. Infection-free and endemic steady states are examined for positivity, boundedness of solutions, and stability. The disease transmission is reduced through non-pharmaceutical interventions as well as the infected rodent populations are controlled by integrated pest management. Using sensitivity analysis, we evaluate the effect of parameters' uncertainty. We study the optimal conditions to reduce bacterial density in the environment by considering control variables as chemical disinfectants and treatment functions. Numerical simulations confirm the theoretical findings.