Deterministic and Stochastic SIS Model of Common Cold in Universiti Malaysia Perlis

Abstract

The epidemiological of common cold with Susceptible‐ Infected‐ Susceptible (SIS) model is the description of the dynamics of a disease that is contact transmitted with no long lasting immunity. 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, between the models and to compare the SIS models demography
without pharmacological treatment and with pharmacological treatment. There are two groups tested in SIS model which is 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 efficiently in R program. Then, differential equations will be constructed which described the mean statistics of each process. Hence, the derivation of reproductive number, had been obtained by using the next generation operator method. 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 measures help to minimize the numbers of infected individuals in the population. Therefore, the pharmacological treatment increases the recovery rate and helps them to recover more quickly. Basic reproductive number, 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 as all the models are greater than 1.