The fuzzy epidemic model in the spread of hepatitis B by vaccine administration

Abstract

This study aims to form a mathematical model of the spread of Hepatitis B by vaccine administration using fuzzy number parameters, to discover the basic reproductive numbers formed from this case, and to obtain numerical simulations of cases of the spread of Hepatitis B by giving vaccines. In this study the epidemic model used was MSIR, while the stage was to model the spread of Hepatitis B by giving the vaccine using the parameters of contact or transmission rate in the form of fuzzy numbers. Then, the equilibrium point was determined, and the stability of the epidemic model was analyzed. Furthermore, the basic reproduction numbers of the fuzzy model was determined to perform a model simulation with certain parameters. The study resulted in a fuzzy model with indeterminate parameters of the case i.e. the contact rate in the form of fuzzy numbers with linear membership functions rising classified as low, medium, and high. The proportion of infected individuals was affected by the contact rate; the higher the contact rate, the higher the proportion of infected individuals. The basic reproduction numbers of fuzzy epidemic models were formed with conditions according to the contact rate classified as low, medium, and high. Furthermore, the minimum rate of giving vaccine to prevent and control disease was equal to 0.4592, meaning 4592 out of 10000 newborn babies have been vaccinated. Numerical simulations with certain parameters described the behavior of the model solution i.e. the higher the contact rate, the higher the proportion of infected individuals. In addition, the higher the change of vaccine, the lower the proportion of infected individuals.