The purpose of this research is to develop an alternative method of relative risk estimation based on stochastic discrete time-space model. There are two main methods proposed which are stochastic discrete time-space SIR (Susceptible-Infected-Removed) model and S(ImIf)R (Susceptible-[Infected male]-[infected female]-Removed) according to gender for HIV and AIDS. Firstly, the deterministic compartmental SIR model that is suitable for the transmission of HIV and AIDS is discussed. This model then is adapted to develop corresponding discrete time-space stochastic SIR model. This is followed by the discussion of the alternative method of relative risk estimation based on the stochastic SIR model. Furthermore, applications of the common methods such as SMR and Poisson-gamma using HIV and AIDS data from Malaysia is also discussed in this thesis and the results are compared in tables, graphs and maps. Subsequently, discussion on modelling of S(ImIf)R model based on gender is discussed in the .....

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Leptospirosis 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 .....

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