Mathematical model of hepatitis B in the Bosomtwe district of Ashanti region, Ghana

Abstract

We use SIR model to predict the prevalence and incidence of Hepatitis B in Bosomtwe District of Ghana. The study is made up of two sections. An SIR model without vaccination is used to explain the spread of the HBV in the Bosomtwe district followed by the modeling HB with vaccination in the district. 3344 Isaac Kwasi Adu et al. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number () of HB without vaccination is estimated to be 1.006 and the basic reproductive number () of HB with vaccination is estimated to be 0.9840. Our work shows that, the proportion of the population of Bosomtwe district that needs to be vaccinated in order to control HBV in the district is 871. According to the results of this study, whenever the transmission rate parameter value is increased, but when the transmission rate parameter value is reduced,. A combination of increased vaccination of newborns and immunization of susceptible adults appears to reduce HB prevalence in Bosomtwe District to the minimum.

A Mathematical Model of the Dynamics of Hepatitis B Virus HBV Infection with Controls

“…The rate at which non-vaccinated susceptible individuals who use condom are being exposed to the infection due to error in condom/condom usage; Denote the rate constant at which susceptible individuals who are not vaccinated and does not use condom move to exposed class 1 The rate of exposed (infected) individuals who obtain treatment; 2 The rate of exposed (infected) individuals who had spontaneous recovery; 1 − 1 The rate at which exposed individuals do not obtain treatment and moves to infectious class;…”

A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination

“…In the last 10 years, many researchers have been using mathematical model to study the dynamics of HBV transmission. For example, the authors (Adu, Aidoo, Darko, & Osei-Frimpong, 2014;Akbari, Kamyad, & Heydari, 2016;Aniji, Kavitha, & Balamuralitharan, 2019;2014;Khan & Zaman, 2016;Kimbir, Aboiyar, Abu, & Onah, 2014;Nana-Kyere, Ackora-Prah, Okyere, Marmah, & Afram, 2017;Nayeem & Podder, 2014;Seyoum Desta & Koya, 2019;Shaban & Manoza, 2016;Shi, Lu, & Wang, 2019;Wiah, Makinde, & Adetunde, 2015;Zhang, Guo, & Smith, 2018;Zou, Zhang, & Ruan, 2010) propose mathematical model of HBV transmission dynamics. However, most these works did not consider both the effect of memory using fractional order derivatives and age structure model simultaneously.…”