Analysis of an SEIR model with the vertical transmission on transmission and spread of hepatitis B in Ghana

Authors

Kwaafo Akoto Awuah-Mensah, Edith Cowan UniversityFollow
Ute Mueller, Edith Cowan UniversityFollow
Steven Richardson, Edith Cowan UniversityFollow

Document Type

Journal Article

Publication Title

Australian Journal of Basic and Applied Science

Publisher

AENSI Publications

School

School of Science

RAS ID

72723

Funders

ECUPRS International Postgraduate scholarship of Edith Cowan University

Comments

K.A. Awuah-Mensah, Ute Mueller, S. Richardson. (2022). Analysis of an SEIR model with the vertical transmission on transmission and spread of hepatitis B in Ghana. Australian Journal of Basic and Applied Sciences, 16(9), 1-11. http://www.ajbasweb.com/old/Ajbas_September-2022.html

Abstract

Lack of good quality information about hepatitis B (HB) is a major hindrance to policy direction and comprehensive implementation of interventions to prevent and control the disease in the endemic region of Sub- Saharan Africa (SSA), particularly Ghana. A SEIR deterministic compartmental model which incorporates latent period and vertical transmission, and applied to HB incidence data was used to examine the transmission and spread of HB in order to inform policy decision on prevention and control of the disease in a population. The model parameters were estimated by a unique hybrid optimisation method involving Genetic Algorithm and Levenberg Marquardt Algorithm using MATLAB (version R2018a). Based on the estimated parameters, the epidemiological threshold parameter ���� was calculated to determine the prediction of the disease. The model was found to have a disease-free equilibrium that is globally asymptotically stable when the epidemiological threshold parameter ���� ≤ ��, and an unique endemic equilibrium that is asymptotically stable when ���� > ��. Stability of the model was discussed in terms of proportions of the state variables, where disease eradication or persistence meant the total infected proportions �� + �� vanished or uniformly persisted respectively with time. The threshold parameter, based on the estimated parameters, was calculated to be ���� = ��. ��������, which indicated that ���� persists in the population. The endemic equilibrium state ��∗ = (��. ��������, ��. ��������, ��. ��������) was stable with total infected proportion 0.4.3 of the population uniformly persisting with time. Vertical transmission was found to be the major drive to transmission and spread of HB, compared with other parameters, and achieving a herd immunity threshold �� = ��. �������� of the population would keep the disease under control. The study also revealed that latent period is important in modelling HB.

DOI

10.22587/ajbas.2022.16.9.1

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.