A DETERMINISTIC MATHEMATICAL MODEL AND ANALYSIS OF THE TRANSMISSION DYNAMICS OF HEPATITIS B VIRUS IN NIGERIA

Abstract

HBV is a serious liver infection caused by hepatitis B virus that can easily be preventable by a vaccine. Nigeria is one of the countries with the highest incidence of HBV infection in the world with less than 23 million Nigerians are estimated to be infected with the Hepatitis B virus (HBV) from a population of two hundred million. The aim of this research work is to modeled HBV by incorporating vaccination, on the sport treatment, sanitarium and immigration into to already exiting SEIR model; the objectives are: to obtain the equilibria state of the model. Analyze local and global stability of the equilibria state and also carry out numerical simulations of the model. We used a deterministic mathematical model of HBV transmission dynamics to demonstrate the dynamics of the disease. We partitioned the population into 7 compartments namely: Immunized M(t), Susceptible S(t), Latent L(t), Infectious I(t), Senatorium S_1 (t), Vaccinated V(t) and Recovered R(t). The dynamics among the compartments are described using differential equations. Epidemiologically this means that HBV disease will continue to persist if immigration HBV infective is not controlled. The local stability of disease-free equilibrium of the dynamical system in the absent of HBV infective immigrant has a reproductive number less than one, readily observed from the coefficient of the polynomial characteristics satisfied the condition Routh-Hurwitz criterion, thus, it is locally asymptotically stable. The global stability of the disease-free equilibrium of the model was obtained and it revealed that, the entries of the matrix for infected compartment G(X,Z) are stickily positive. Hence, the global stability of the disease free is stable. In order to ascertain the impact of using vaccination or sanatorium or combination of both control strategies on fighting HBV, we established a baseline values for the parameters and implored the use of MATLAB Codes in computing numerical values, the results shows that the infected population is significantly higher than the other population densities even when vaccination is administered in relatively small amount. When the vaccination rate is increased to , the infected population drastically declined and vice versa.