Stability Analysis of Monkeypox Transmission Model by Administering Vaccine - Lailatuz Arromadhani; Budi Priyo Prawoto (Institut Agama Islam Ma'arif NU (IAIMNU) Metro Lampung, 2023)
Monkeypox is an infectious disease that affects mammals, including humans and some primates. Monkeypox transmission can be prevented by administering vaccinations to the human population. This study aims to construct and analyze the monkeypox transmission model's stability with vaccination. There are six sub-populations: Vaccinated humans ( ), Susceptible humans ( ), Infected human , Recovered human , Susceptible animal , and Infected human . Several steps are literature study, formulating assumptions, constructing models, finding equilibrium points, searching for reproduction numbers by next-generation matrix, analyzing stability, and numerical simulations using Matlab R02023b. From the model, three equilibria are obtained: disease-free equilibrium points, first endemic equilibrium points, and second endemic equilibrium points. Disease-free equilibrium point will be asymptotically stable at the vaccination rates and the animal transmission rate of the animal at the rate of . The first endemic equilibrium point ) will be stable for and . The second endemic equilibrium point will be stable for and . Based on numerical simulation results, it is obtained that the higher the vaccination rate and the lower the transmission rate in animals, the faster the transmission of monkeypox infections.