Mathematical modelling of the spread of Leptospirosis

Abstract

Leptospirosis is an infectious disease caused by bacteria belonging to genus Leptospira. Leptospirosis occurs worldwide, but is most prevalent in tropical and subtropical regions. Outbreaks can occur following excessive rainfall or flooding. The transmission of this disease is studied through mathematical model. Two case studies are discussed in this research. The first case study is a modification of simple Susceptible-Infected-Removed (SIR) model involving human and vector populations whereas for the second case study, we incorporate the idea of classifying the human into two classes, namely juvenile and adult into the Leptospirosis transmission model. Two equilibrium points are found and the stability conditions for these equilibrium points are established. Numerical solutions of the model are conducted. The results of this study guide the way to decrease the disease outbreak.