Dynamical Analysis and Parameter Estimation of Hepatitis B Disease Model in Malang

Fitroh Aulani, Wuryansari Muharini Kusumawinahyu, Isnani Darti



In this article, a model representing the spread of Hepatitis B disease is constructed as a nonlinear autonomous system. The model divides the considered human population into three classes, namely susceptible, infected, and recovered class. The dynamical analysis shows that there are two equilibrium points in the model, namely a disease-free equilibrium point and an endemic equilibrium point. The existence and stability of the equilibrium points depend on the basic reproduction number (R_0). The disease-free equilibrium point is local asymptotically stable when R_0<1 while the endemic equilibrium point exists and is local asymptotically stable if R_0>1. The five parameters of the model are estimated by applying Downhill Simplex (Nelder-Mead) Algorithm and by using the infected data cases taken from such a hospital in Malang. The estimated parameters are the transmission of infection rate, the saturation rate, the vaccination rate, the recovery rate, and the immunity loss rate. The resulting parameter estimation supports the analytical result and is used to illustrate the analytical results numerically. Based on the considered model and the result of the parameters estimation, it can be concluded that the Hepatitis B spread in Malang is controllable.

Keywords: downhill simplex (Nelder-mead) algorithm, dynamical analysis, hepatitis B model, parameter estimation. 

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DOI: http://dx.doi.org/10.21776/ub.jels.2021.011.03.03


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