Dynamical Analysis and Optimal Control of SVIR Hepatitis B Model Spread in Malang

Pangestuti Prima Darajat (Universitas Islam Raden Rahmat Malang)
Bagus Seta Inba Cipta (Universitas Islam Raden Rahmat Malang)
Iqbal Farhan Nuruddin (Universitas Islam Raden Rahmat Malang)
Davina Aulia Iqbiyana Balqis (Universitas Islam Raden Rahmat Malang)

Vygotsky: Jurnal Pendidikan Matematika dan Matematika
Vol 5 No 2 (2023): Vygotsky: Jurnal Pendidikan Matematika dan Matematika

This research formulates a new mathematical model that describes the dynamics of the spread and control of Hepatitis B, especially in Malang, East Java. The mathematical model that will be constructed considers various factors in Malang, mainly the saturated Incidence rate and vaccinations carried out on newborns. The equilibrium point of the system is determined and its stability is dynamically analized. The results of this analysis will determine the future prediction of the spread of Hepatitis B in Malang. Furthermore, a control strategy is proposed that is Clean and Healthy Living behavior (PHBS). The control strategy is analysed using optimal control theory. Pontryagin’s principle is used as a condition to obtain optimal conditions. Forward-backwards Sweep method in combination with the fourth order Runge-Kutta method is used to solve the optimal system.