A compartmental model for leptospirosis disease control via vaccination and chlorination

This study develops a mathematical model to investigate the transmission dynamics of leptospirosis in humans and the environmental dynamics of Leptospira in water and soil contaminated by infected rodents. The model also incorporates the relatively rare human-to-human transmission pathway alongside dominant zoonotic routes. It distinguishes between anicteric and icteric clinical forms, includes human vaccination and treatment strategies, and accounts for chlorination of contaminated water as a control measure. Epidemiological data from 2020 to 2025, obtained from the Thiruvananthapuram district, Kerala, India, are used to support the parameterization and analysis of the proposed mathematical model. The basic reproduction number is calculated as R₀ = 1.0621 using the next-generation matrix approach, indicating disease persistence. Both local and global stability analyses of the disease-free and endemic equilibria are performed. Sensitivity analysis identifies the transmission parameters β ₂ and β ₃ , treatment/recovery parameter γ ₂ , vaccination effectiveness v , vaccination rate ρ , and chlorination rate χ as key parameters influencing disease transmission. Numerical simulations demonstrate that the proposed control strategies can reduce R₀ below unity, thereby effectively limiting the spread of Leptospira .