# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology

8-12 July 2018
Australia/Sydney timezone

## SEIVR epidemic model (Susceptible, Exposed, Infected, Vaccinated and Recovered) on the spread of hepatitis B disease

Not scheduled
20m
Oral Presentation Disease - infectious

### Speakers

Mr Fatkhur RohimMr Bimanto Bayu BintoroMr Yahya Nur Marfuad

### Description

Hepatitis B is a disease caused by the hepatitis B virus. It’s generally divided into 3 categories namely healthy carrier, acute hepatitis, and chronic hepatitis. The spread of hepatitis B disease can be modelled in a mathematical model. We develop the mathematical model to describe the spread of hepatitis B. We modify the model of SEIV by introducing recovery class into the model (SEIVR model). The behaviour of the dynamics model is analyzed to investigate the positivity and boundedness solutions, and the stability of equilibrium points. Basic reproduction number ($R_{0}$) is derived from next generator matrix to determine the stability of equilibrium point and endemicity of hepatitis B disease in long term. The disease free equilibrium point is locally asymptotically stable if $R_{0}$<1, unstable $R_{0}$>1. The endemic equilibrium point is locally asymptotically stable if $R_{0}$<1 and unstable if $R_{0}$>1. Simulation results are presented to provide the description of the analysis results.

### Presentation Materials

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