Mathematical Model and Analysis of Leptospirosis Transmission Dynamics in Human and Dog Populations.
DOI:
https://doi.org/10.62054/ijdm/0303.24Abstract
Leptospirosis is a zoonotic disease caused by Leptospira species and remains a major public health concern in tropical and subtropical regions. It is transmitted primarily through contact with contaminated water or soil. This study develops and analyzes a mathematical model of the transmission dynamics of leptospirosis to enhance understanding of its spread. The basic reproduction number was derived using the next-generation matrix (NGM) method to quantify the average number of secondary infections. The local and global stability of the system were established using the Routh–Hurwitz criterion and the Castillo–Chavez method, respectively. It was shown that the disease-free equilibrium is both locally and globally asymptotically stable when , while the endemic equilibrium remains globally asymptotically stable when , using a Goh–Volterra-type Lyapunov function. Sensitivity analysis was performed using the normalized forward sensitivity index to identify key parameters influencing disease transmission. Parameters with positive sensitivity indices increase the risk of outbreaks, whereas those with negative indices reduce the likelihood of sustained transmission. Numerical simulations were conducted to illustrate the effects of these parameters and to evaluate intervention strategies. The results indicate that effective control of leptospirosis requires a combination of improved environmental sanitation and proper treatment of infections in both humans and animals, providing valuable insights for public health policy in affected communities.
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