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ANALYSIS OF A STOCHASTIC HBV INFECTION MODEL WITH NONLINEAR INCIDENCE RATE
Journal of Biological Systems ( IF 1.3 ) Pub Date : 2019-10-21 , DOI: 10.1142/s0218339019500177
HONGWEN HUI 1 , LIN-FEI NIE 1
Affiliation  

Considering that environmental factors, diet, subconscious mind and other uncertainties play an important role in the process of delaying and treating diseases, we propose, in this paper, an amended Hepatitis B virus (HBV) model with stochastic perturbation, and investigate the longtime dynamics of this stochastic model. First, if the basic reproductive number of the corresponding deterministic model is less than 1, some sufficient conditions for almost surely exponentially stable in the sense of the infected cells and free virus are established, and the stationary probability density function of the uninfected sell is also obtained. Further, some sufficient conditions for the existence of the stationary distribution are obtained for the basic reproductive number more than 1. In addition, oscillatory behaviors of this model about the equilibrium of the corresponding deterministic model are discussed. Finally, numerical simulations demonstrate the main theoretical results and show stochastic virus model has more dynamic behaviors relative to its corresponding deterministic model. Theoretical results and numerical simulations imply that the intensity and “type (divided into positive and negative)” of white noise play very important roles in the treatment of infectious disease, which can make the disease more and more repetitive and unpredictable. Of course, comfortable environment, reasonable diet, optimistic mood and other positive uncertainty factors have active effects on the treatment and delaying of diseases, but not the converse.

中文翻译:

具有非线性发病率的随机 HBV 感染模型的分析

考虑到环境因素、饮食、潜意识等不确定因素在疾病的延缓和治疗过程中发挥着重要作用,本文提出了一种带有随机扰动的修正乙型肝炎病毒(HBV)模型,并研究了其长期动态。这个随机模型。首先,如果相应确定性模型的基本再生数小于1,则在感染细胞和游离病毒意义上几乎肯定指数稳定的一些充分条件成立,未感染细胞的平稳概率密度函数也为获得。进一步,对于大于1的基本再生数,得到了存在平稳分布的一些充分条件。另外,讨论了该模型关于相应确定性模型平衡的振荡行为。最后,数值模拟证明了主要的理论结果,并表明随机病毒模型相对于其相应的确定性模型具有更多的动态行为。理论结果和数值模拟表明,白噪声的强度和“类型(分为阳性和阴性)”在传染病的治疗中起着非常重要的作用,它可以使疾病越来越重复和不可预测。当然,舒适的环境、合理的饮食、乐观的情绪等积极的不确定因素对疾病的治疗和延缓有积极作用,但反之则不然。数值模拟证明了主要的理论结果,并表明随机病毒模型相对于其相应的确定性模型具有更多的动态行为。理论结果和数值模拟表明,白噪声的强度和“类型(分为阳性和阴性)”在传染病的治疗中起着非常重要的作用,它可以使疾病越来越重复和不可预测。当然,舒适的环境、合理的饮食、乐观的情绪等积极的不确定因素对疾病的治疗和延缓有积极作用,但反之则不然。数值模拟证明了主要的理论结果,并表明随机病毒模型相对于其相应的确定性模型具有更多的动态行为。理论结果和数值模拟表明,白噪声的强度和“类型(分为阳性和阴性)”在传染病的治疗中起着非常重要的作用,它可以使疾病越来越重复和不可预测。当然,舒适的环境、合理的饮食、乐观的情绪等积极的不确定因素对疾病的治疗和延缓有积极作用,但反之则不然。理论结果和数值模拟表明,白噪声的强度和“类型(分为阳性和阴性)”在传染病的治疗中起着非常重要的作用,它可以使疾病越来越重复和不可预测。当然,舒适的环境、合理的饮食、乐观的情绪等积极的不确定因素对疾病的治疗和延缓有积极作用,但反之则不然。理论结果和数值模拟表明,白噪声的强度和“类型(分为阳性和阴性)”在传染病的治疗中起着非常重要的作用,它可以使疾病越来越重复和不可预测。当然,舒适的环境、合理的饮食、乐观的情绪等积极的不确定因素对疾病的治疗和延缓有积极作用,但反之则不然。
更新日期:2019-10-21
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