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

Hardiyanti, R. Ratianingsih, Hajar
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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.
水痘和带状疱疹是由水痘带状疱疹病毒引起的两种人类传染性皮肤病,其中水痘是一种原发性感染,常感染年轻人,而带状疱疹是一种复发性疾病,由于水痘带状疱疹潜伏病毒的再活化,常感染老年人。如果带状疱疹引起的疼痛在复发期后才出现,那么这种情况被称为带状疱疹后神经痛。本研究在SIR模型(易感、感染、恢复)的基础上建立了原发性感染(水痘病)和复发性感染(带状疱疹病)的数学模型。人群分为易感人群、感染人群、水痘恢复期人群、带状疱疹人群和带状疱疹后神经痛人群7个亚群。用线性化方法对临界点进行稳定性分析,给出了一个保证存在且不稳定的临界点𝑇1,而临界点𝑇1没有任何要求。表示地方病无病临界点的稳定性分析𝑇1,如果𝑇2存在,稳定性分析𝑇1,如果𝑇2存在,稳定性分析𝑇1。通过数值模拟来模拟这种暂时的无病状态和地方性的稳定状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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