Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana
Ali Abubakar *
Department of Mathematics, Nkrumah University of Science and Technology, Kumasi, Ghana.
Reindorf Nartey Borkor
Department of Mathematics, Nkrumah University of Science and Technology, Kumasi, Ghana.
Anas Musah
Department of Mathematics, Nkrumah University of Science and Technology, Kumasi, Ghana.
Frank Kofi Owusu
Department of Mathematics, Nkrumah University of Science and Technology, Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
The paper evidenced that Hepatitis B infection is the world's deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.
Keywords: Hepatitis B, susceptible, exposed, differential equation, epidemiology, infectious diseases, vaccination rate