Open AccessGlobal stability of varicella model
Author(s) -
Edwin Setiawan Nugraha,
Dayat Hidayat
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1722/1/012034
Subject(s) - vaccination , disease , intervention (counseling) , basic reproduction number , stability theory , mathematics , lyapunov function , medicine , virology , environmental health , physics , population , nonlinear system , quantum mechanics , psychiatry
Varicella is a disease caused by the varicella-zooster virus. This disease is common in children under 10 years of age and is not a fatal condition. However, some cases of varicella in adults are more dangerous because they can cause pneumonia. Here, discussion about analysis of varicella epidemic model is presented. This model is expressed in the form of 6th order differential equation with state variables as follows susceptible, exposed, infected, quarantine, recovered, and vaccination. Apart vaccination and isolation intervention, this model also consider disinfectant spray an¡d ventilation. Our analysis shows that varicella dynamic behavior depends on the basic reproduction number ( R 0 ). The model has two equilibria, namely, free disease and endemic equilibria. By using the Lyapunov function, we demonstrate that when R 0 ≤1, disease-free is globally asymptotically stable, and when R 0 > 1 disease-free becomes unstable while endemic is globally asymptotically stable. This results indicate more effective each intervention, the better the control of varicella.