Analisis Model Matematika Penyebaran Virus Hanta pada Populasi Tikus dan Manusia
DOI:
https://doi.org/10.30605/proximal.v9i2.9308Keywords:
Virus Hanta, Model Matematika, Kestabilan, Titik EkuilibriumAbstract
Hanta virus is a zoonotic disease transmitted from rodents, which serve as its natural reservoir, to humans and may cause severe health complications. Therefore, mathematical modeling is an important approach for understanding the transmission dynamics and supporting effective disease control strategies. This study aims to analyze the transmission dynamics of Hantavirus using a SI–SIR compartmental model involving interactions between rodent and human populations. The proposed model is formulated as a system of nonlinear ordinary differential equations that incorporates both rodent-to-rodent and rodent-to-human transmission. The main contribution of this study is the development of a two-population mathematical model that integrates transmission dynamics in the reservoir and human populations, followed by an analytical investigation of its dynamical behavior. The model admits two equilibrium points, namely the disease-free equilibrium and the endemic equilibrium. The basic reproduction number ( ) is derived using the Next-Generation Matrix (NGM) method, while the local stability of the disease-free equilibrium is analyzed through the eigenvalues of the Jacobian matrix. The analytical results show that the disease-free equilibrium is locally asymptotically stable whenever , whereas the endemic equilibrium exists when . Furthermore, numerical simulations are performed to illustrate the effects of transmission parameters on the system dynamics and to validate the theoretical findings.
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