Modelling Vertical Transmission Of Hepatitis B Virus In An Age-Structured Population In The Presence Of Treatment In Nigeria

An age-structured SIR compartmental model of Hepatitis B Virus (HBV) dynamics that incorporates vertical transmission and the effect of Treatment is developed. The model equations were first transformed into proportions, thus reducing the model equations from eight to six differential equations. The model is analyzed for the existence and stability of the disease-free equilibrium (DFE) state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number R
₀
<; 1 and the following threshold conditions (R
₁
<; 1, R
₂
<; 1, R
₃
<; 1, R
₄
<; 1, R
₅
<; 1, R
₆
<; 1, R
₇
<; 1 and R
₈
<; 1) are satisfied. This invariably is biologically interpreted to mean that eradication of the disease is possible in finite time under these conditions. Furthermore, the model was solved numerically using Runge- Kutta Fehlberg method of order four and numerical simulations carried out yields interesting results. Baseline data and parameters for Nigeria were use in the numerical simulation. Results in this paper suggest that high treatment rate should not be done in isolation; rather it should be combined with behavioral interventions which will reduce the prevalence of the infection. Mother to child (MTC) transmission of HBV can be reduced to the barest minimum if the probability of transmission from adult to adult and mother to child is significantly reduced to zero. To achieve this, education and counselling of both susceptible and infected juvenile and adults will go a long way to reduce the probability of transmission to the barest minimum. Finally, susceptible children must also be assisted to retain their current status via continuous counselling and education as the mature to susceptible adult at the rate of η
_s
.