Model Matematika Infeksi Hepatitis B dengan Vaksin dan Pengobatan
DOI:
https://doi.org/10.31316/j.derivat.v12i3.8256Abstract
A worldwide public health concern, hepatitis B is brought on by an infection with the Hepatitis B Virus (HBV). HBV can spread when an infected person's blood or bodily fluids come into contact with you. Prevention of HBV infection can be done through two doses of HBV vaccination. Hepatitis B sufferers experience two phases of infection, namely the acute phase and the chronic phase. Hepatitis B sufferers who have entered the chronic phase require treatment to improve recovery. This study aims to model the dynamics of the spread of hepatitis B with the presence of vaccines and treatment. The mathematical model developed consists of seven subpopulations, namely: susceptible (S), first dose vaccine (V1), second dose vaccine (V2), acute (A), chronic (C), treatment (T), and recovered (R). Two equilibrium points are produced by model analysis: the endemic equilibrium point (E1). and the disease-free equilibrium point (E0). The Next Generation Matrix was used to get the Basic Reproduction Number (R0). The analysis's findings suggest that hepatitis B transmission does not spread if R0, as this indicates that the disease-free equilibrium point (E1) is locally asymptotically stable. Conversely, if R0 , then the disease-free equilibrium point (E0) is locally asymptotically unstable, resulting in infection in the susceptible population (S). The dynamics of the mathematical model is demonstrated by numerical simulations.
Keywords: Hepatitis B Virus; Mathematical Model; vaccination; treatment.
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