Analisis Kestabilan Global dan Analisis Sensitivitas pada Model Matematika Penyebaran Penyakit Gondongan
Abstract
Mumps is a contagious viral disease transmitted through respiratory droplets and close contact. It can cause symptoms like fever and salivary gland swelling. Despite the MMR vaccine, which offers partial protection, outbreaks persist, especially in college-aged individuals. Epidemiological models can aid in identifying effective prevention strategies for controlling mumps transmission. This paper proposes a mathematical model for mumps spread, considering quarantined individuals and complications. A global stability analysis of the mumps transmission model was performed, considering mortality and quarantine subpopulation. The Disease Free Equilibrium and Endemic Equilibrium Point are globally stable, confirmed by Lyapunov functions. Sensitivity analysis of the basic reproduction number shows that reducing birth rates and contact between infected and susceptible individuals effectively minimizes the infected population. However, increasing the natural death rate can reduce the total population, which may lower infections, but poses potential social and economic challenges for decision-makers.
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