Mathematical model of leptospirosis in Malaysia using the SIR approach

Leptospirosis is the most common zoonotic infection in tropical areas. Leptospirosis has become an endemic disease in Malaysia since 2010, caused by bacteria called pathogenic spirochetes of the genus leptospira. Infected animals' urine spreads the bacteria, which can enter water and soil and live for weeks or months. If you encounter soil or water where an infected animal has peed, the germ can enter your body through skin breaks such as scratches, open wounds, or dry areas. Leptospirosis is a growing public health problem, and if not adequately managed, it might have a significant health impact and burden on the country in the coming years. Numerous mathematical models of infectious diseases have been formulated. The SIR model is one of the mathematical models that has proven to be useful in analysing infectious diseases. However, there has been a minimal study on the dynamics of leptospirosis cases using the SIR model, particularly in Malaysia. Hence, this study aims to formulate a mathematical model of leptospirosis transmission in Malaysia using the SIR model. The SIR model is expressed as a set of first-order ordinary differential equations. The obtained results reveal that the basic reproduction number (R₀) for the model is lower than one, which indicates that leptospirosis is endemic in a population. In addition, the local stability analysis of the disease-free equilibrium point is also presented and discussed. The numerical analysis in this study was carried out using Matlab software. The result is graphically plotted, showing that the SIR-SI model of leptospirosis cases in Malaysia demonstrates that leptospirosis has become endemic.