A stochastic approach to leptospirosis disease in human and vector populations: Analysis, dynamics and validation with world wide real data

Leptospirosis is a bacterial infection transmitted through contact with water contaminated by the urine of infected animals, often affecting both humans and animals, particularly in tropical and subtropical regions. This paper illustrates a stochastic model for the transmission dynamics of leptospirosis infections in both human and vector populations. The model enhances key factors such as rainfall impact, vector behavior, and human interactions to capture the transmission of the disease. Through detailed mathematical investigation, the article explains the criteria required for the existence and uniqueness of a global solution for the stochastic model. Nonlinear analysis notions are utilized to investigate the ergodic aspects of the stochastic model. To validate the model's effectiveness, numerical simulations are conducted, and the results are compared with deterministic behavior. The comparison highlights the importance of considering stochasticity in accurately capturing the dynamics of leptospirosis. The paper also illustrates the relevance of the proposed system by comparing the model's dynamics with real-world leptospirosis cases globally. This validation displays the model's ability to capture the epidemiological characteristics and trends observed in different geographical regions. Moreover, the impact of the rate of transmission of leptospirosis from an infected vector to a susceptible human on the evolution of infected individuals within the population is visualized, delivering insightful information. Major outputs of the study include the identification of critical parameters influencing disease spread and the demonstration of the stochastic model's superior accuracy over deterministic approaches in reflecting real-world scenarios.