The epidemiological with SIS model is the description of the dynamics of a disease that is contact transmitted with no long lasting immunity. Common cold can be categorized as a SIS model. This illness caused by a virus infection located in the nose and the virus is transmitted to individuals. They will recover with no immunity to the common cold and immediately susceptible once they have recovered. This is the first attempt to develop SIS model on common cold. The purpose of this study is to compare between the deterministic and stochastic SIS model with demography and without demography (presence of births and deaths), to derive the reproductive number, 𝑅0 between the models and to compare the SIS models demography without pharmacological treatment and with pharmacological treatment. There are two groups tested in SIS models which are UNIMAP’s students and UNIMAP’s staffs and these data were taken from UNIMAP’s university health centre on September 2015. In this study, SIS models were implemented as set of deterministic ordinary differential equations (ODE) that can be solved by using different numerical methods and a discrete time Markov chain (DTMC) process in stochastic simulations. Gillespie algorithm had been used to generate stochastic simulations very efficiently in R program by drawing a random process from all events in process according to their respective probabilities. Then, differential equations will be constructed which describe the mean statistics of each process. Hence, the derivation of reproductive number, 𝑅0 had been obtained by using the next generation operator method and defined as ‘the expected number of secondary cases produced, in a completely susceptible population, by a typical infective individual’. In these cases, the number of infected persons in SIS demography will continuously decrease as there are presence of births and deaths in the population. Pharmacological treatment had been used to improve and control the infection of common cold from spread to population. This control measure help to minimize the number of infected individuals in the population. The dynamics of deterministic and stochastic discrete time Markov Chain (DTMC) SIS models with and without pharmacological treatment are determined and compared by using different parameter values of recovery rate to obtain the behaviour of infected population. Therefore, the pharmacological treatment increases the value of recovery rate and help them to recover more quickly. Other than that, basic reproductive number, 𝑅0 for every models without demography and with demography were derived for determining whether a disease persist in the population or not. The disease will continuously spread out into population if 𝑅0 > 1 as all the models are greater than 1.
