ANALYSIS OF THE EFFECT OF RELAPSE FOR EPIDEMIC MALARIA TRANSMISION DESEASE USING STOCHASTIC SIRS MODEL IN KOLA DIBA, NORTH GONDAR, NORTHWEST ETHIOPIA

The objective of this study is to analyze the dynamics of malaria transmission and show how relapse affects malaria infected people using a stochastic model, particularly a simple SIRS model. A stochastic model with the Markov property describes the dynamics of malaria and human population in terms of stochastic equations. It is carried out by estimating the malaria relapse rate and the reproduction number. In this work, we used certain assumptions and presenting the SIRS model, implemented on Python language with their transition diagrams. The population dynamics are modelled by the SIRS model, which assumes only a plasmodium vivax malaria in which pseudo recovered persons can recover and return to the susceptible class or relapse and become infectious again. The results suggest that SIRS model is effective model for studying malaria transmission model with relapse and the reproduction number, R_0 >1, implying an epidemic. Reproduction number and infective population are increasing with respect to the relapse rate and the study area is under the influence of malaria transmission; and experiences the probability of an outbreak. Subject: Infectious Disease, Global Health, Health Informatics and Statistical and Computational Physics Key words: SIRS model, relapse rate, stochastic model, basic reproduction number, Markov chain, epidemic.