AbstractLeptospirosis is a re-emerging global disease that has become endemic in Malaysia. The transmissions usually occur between animals especially rats to rats and rats to humans. Since, it is an easily contractable disease that can be transmitted directly through contact with infected rats urine or indirectly from the environment such as via water and soil, it is very challenging to curb this disease from infecting humans. Poor understanding of the disease and lack of epidemiological data also made leptospirosis is difficult to control. To cope with this problem, a leptospirosis disease transmission model is developed to study the mechanism of leptospirosis disease spread over continuous-time that may help to predict future caused of an outbreak. This study aims to construct a continuous-time and discrete-space stochastic SIR-L-SI (Susceptible, Infected, Recovered Humans-Leptospires in the Environment-Susceptible, Infectious Rats) of leptospirosis disease transmission to estimate the risk .....