Examining HIV progression mechanisms via mathematical approaches

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2020-12-05 DOI:10.5206/mase/10774
Wenjing Zhang, Ramnath Bhagavath, N. Madras, J. Heffernan
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引用次数: 1

Abstract

The progression of HIV infection to AIDS is unclear and under examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune system cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We show that both formulae are equivalent. We derive analytical conditions for the occurrence of backward and forward bifurcations. To investigate the influence of the proposed mechanisms to the HIV progression, we perform uncertainty and sensitivity analysis for all parameters and conduct a bifurcation analysis on all parameters that are shown to be significant, in combination, to explore various HIV/AIDS progression dynamics.
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通过数学方法研究HIV进展机制
艾滋病毒感染到艾滋病的进展尚不清楚,尚待研究。许多机制被提出,包括免疫应答下降、复制速率增加、胸腺退化、合胞体诱导能力、潜伏感染细胞池的激活、免疫系统的慢性激活以及病毒感染其他免疫系统细胞的能力。每种机制联合作用的意义尚未得到研究。我们开发了一个简单的HIV病毒动力学模型,将提出的机制作为允许变化的参数。在整个参数空间中,我们分别从单个CD4 T细胞和单个病毒粒子开始考虑感染,推导出基本繁殖数(R0)的两个公式。我们证明两个公式是等价的。我们导出了前向分岔和后向分岔发生的解析条件。为了研究所提出的机制对HIV进展的影响,我们对所有参数进行了不确定性和敏感性分析,并对所有被证明是重要的参数进行了分岔分析,结合起来探索各种HIV/AIDS进展动态。
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来源期刊
CiteScore
1.40
自引率
0.00%
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0
审稿时长
21 weeks
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