Kestabilan Model Matematika Infeksi Primer Penyakit Varicella Dan Infeksi Rekuren Penyakit Herpes Zoster Oleh Virus Varicella Zoster

Abstract

Varicella and herpes zoster are two infectious skin diseases of human that caused by varicella zoster virus, where varicella disease is a primary infection that often infected younger people while herpes zoster disease is a recurrent disease that often infected older people because of reactivation of latent varicella-zoster virus. If the pain caused by herpes zoster after recurrent phase is a appeared then the condition is known as postherpetic neuralgia. This study builds a mathematical model of primary infection (varicella disease) and recurrent infection (herpes zoster disease) developed from the SIR model (Susceptible, Infected, Recovered). The human population is divided into seven subpopulations, namely susceptible, infection, recovered of varicella, herpes zoster and postherpetic neuralgia subpopulation. Stability analysis at the critical point by linearization method gives a critical point 𝑇1 that guaranted to exist and unstable if 𝛼 𝜇(𝛽1+𝜇) 𝐴 , while the critical point 𝑇1 does not have any reqruitment. Stability analysis at the endemic disease-free critical point is represented 𝑇1 that will be unstable if 𝑇2 exist and stable 𝑇1 if 𝑇2 exist. Numerical simulations by simulated to describe such temporary disease-free conditions and an endemic stable conditions.