Author Identifier

Kwaafo Akoto Awuah-Mensah

Date of Award


Document Type



Edith Cowan University

Degree Name

Doctor of Philosophy


School of Science

First Supervisor

Associate Professor Ute Mueller

Second Supervisor

Dr Steven Richardson


The world's attention to the burden and spread of hepatitis B has increased signicantly in the recent past. A number of interventions by way of treatment and immunisation have been initiated to fight the pandemic, especially in high prevalence regions such as Africa and Asia. Lack of good quality information about hepatitis B is a major hindrance to policy direction and comprehensive implementation of interventions in Sub-Saharan Africa designated as an endemic region. Limited studies on hepatitis B, coupled with lack of adequate health care systems and infrastructure, have led to ignorance or misconceptions and stigmatisation about the disease and worsened the disease prevalence in Ghana a Sub-Saharan African country. As a contribution, this study employed a SEIR deterministic compartmental model, which incorporates latent period and vertical transmission, to examine the transmission and spread of hepatitis B in the context of the Sub-Saharan Africa with incidence data obtained from Ghana.

The SEIR deterministic compartmental modelling divided the human population into separate classes namely susceptible (S), exposed (E), infectious (I) and removed (R) or recovered, and disease progression among population members in the various classes was described using a system of nonlinear ordinary di_erential equations (ODEs). The model has two equilibrium states namely, the disease-free equilibrium Q0 and the endemic equilibrium Q*. Stability analysis indicated that the model has an epidemiological threshold parameter R0 which is defined as the expected proportion of secondary infections generated as a result of introducing a single infected individual into the population. When R0 ≤1 the disease-free equilibrium state is globally asymptotically stable whilst the endemic equilibrium state is unstable and so the disease is brought under control. When R0 > 1, the disease-free equilibrium is unstable whilst the endemic equilibrium state is stable and so the disease persists in the population. Stability of the model was analysed in terms of proportions instead of the absolute number of cases and so disease eradication or persistence referred to the infected proportions vanishing or persisting respectively. A hybrid nonlinear least squares method, that combines a Genetic Algorithm (GA) and a modifed Levenberg-Marquadt (LM) algorithm, was applied to the hepatitis B incidence data to estimate the parameters of the model for Ghana (global) and also for each of the ten regions of Ghana. By numerical simulations, sensitivity analysis was performed to examine the effects of the model parameters on the threshold parameter R0 using MATLAB. Furthermore, the model was modi_ed to include a vaccination component to examine the impact of an intervention on the transmission and spread of the disease. The vaccination model also has an epidemiological threshold parameter Rv0 such that when the vaccination rate k is greater than a threshold value k*, then Rv0 < 1 and the disease decreases; and when k is less than k*, Rv0 > 1 and the disease increases. This indicated that when the rate of vaccination k was increased beyond the threshold value k*, the disease would be kept under control.

The threshold parameter was calculated as R0 = 1:6854 for Ghana. This indicated that the endemic proportion equilibrium is asymptotically stable and so hepatitis B persists in the population of Ghana. The contact rate β, latency rate and vertical transmission rate γ were identifed as driving the disease spread in the population. A critical proportion of H = 0:4067 was calculated as the herd immunity threshold value of the population. This means that about 41% of the population are needed to be immune in order to adequately reduce the rates of transmission to keep the disease under control. Variability in the regional threshold parameters R0 indicated significant disparities in the spread and burden of hepatitis B across the ten regions of Ghana. The highest and the least values of (R0 = 3:7212;H = 0:7312) and (R0 = 1:3669;H = 0:2684) were calculated for Upper West and Volta regions respectively. The regional threshold parameters R0 also indicated that the trend of transmission and spread of the disease increase from south to north across the regions of Ghana. A simple regression analysis performed indicated that the increasing trend from south to north is highly associated with poverty and health sector differentials. Another factor that was considered in this study to have potentially impacted the distribution and pattern of spread and burden of hepatitis B in Ghana is prevalence differentials among regions and between Ghana and its neighbouring countries.

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Diseases Commons


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