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A diffusive virus model with a fixed intracellular delay and combined drug treatments
Journal of Mathematical Biology ( IF 1.9 ) Pub Date : 2021-07-29 , DOI: 10.1007/s00285-021-01646-7
Feng-Bin Wang , Chang-Yuan Cheng

The method of administration of an effective drug treatment to eradicate viruses within a host is an important issue in studying viral dynamics. Overuse of a drug can lead to deleterious side effects, and overestimating the efficacy of a drug can result in failure to treat infection. In this study, we proposed a reaction-diffusion within-host virus model which incorporated information regarding spatial heterogeneity, drug treatment, and the intracellular delay to produce productively infected cells and viruses. We also calculated the basic reproduction number \({\mathcal {R}}_0\) under the assumptions of spatial heterogeneity. We have shown that the infection-free periodic solution is globally asymptotically stable when \({\mathcal {R}}_0<1\), whereas when \({\mathcal {R}}_0>1\) there is an infected periodic solution and the infection is uniformly persistent. By conducting numerical simulations, we also revealed the effects of various parameters on the value of \({\mathcal {R}}_0\). First, we showed that the dependence of \({\mathcal {R}}_0\) on the intracellular delay could be monotone or non-monotone, depending on the death rate of infected cells in the immature stage. Second, we found that the mobility of infected cells or virions could facilitate the virus clearance. Third, we found that the spatial fragmentation of the virus environment enhanced viral infection. Finally, we showed that the combination of spatial heterogeneity and different sets of diffusion rates resulted in complicated viral dynamic outcomes.



中文翻译:

具有固定细胞内延迟和联合药物治疗的扩散病毒模型

施用有效药物治疗以根除宿主内病毒的方法是研究病毒动力学的一个重要问题。过度使用药物会导致有害的副作用,高估药物的功效会导致无法治疗感染。在这项研究中,我们提出了一种宿主病毒内反应扩散模型,该模型结合了有关空间异质性、药物治疗和细胞内延迟的信息,以产生有效感染的细胞和病毒。我们还在空间异质性的假设下计算了基本再生数\({\mathcal {R}}_0\)。我们已经证明,当\({\mathcal {R}}_0<1\) 时,无感染周期解是全局渐近稳定的,而当\({\mathcal {R}}_0>1\)存在被感染的周期解并且感染是一致持久的。通过进行数值模拟,我们还揭示了各种参数对\({\mathcal {R}}_0\) 值的影响。首先,我们表明\({\mathcal {R}}_0\)对细胞内延迟的依赖性可以是单调的或非单调的,这取决于未成熟阶段受感染细胞的死亡率。其次,我们发现受感染细胞或病毒粒子的流动性可以促进病毒清除。第三,我们发现病毒环境的空间碎片化增强了病毒感染。最后,我们表明空间异质性和不同的扩散率集的结合导致了复杂的病毒动态结果。

更新日期:2021-07-29
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