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Existence and Dynamics of Strains in a Nonlocal Reaction-Diffusion Model of Viral Evolution
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-01-20 , DOI: 10.1137/19m1282234 Nikolai Bessonov , Gennady Bocharov , Andreas Meyerhans , Vladimir Popov , Vitaly Volpert
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-01-20 , DOI: 10.1137/19m1282234 Nikolai Bessonov , Gennady Bocharov , Andreas Meyerhans , Vladimir Popov , Vitaly Volpert
SIAM Journal on Applied Mathematics, Volume 81, Issue 1, Page 107-128, January 2021.
In this work, we develop a mathematical framework for predicting and quantifying virus diversity evolution during infection of a host organism. It is specified as a virus density distribution with respect to genotype and time governed by a reaction-diffusion integro-differential equation taking virus mutations, replication, and elimination by immune cells and medical treatment into account. Conditions for the existence of virus strains that correspond to localized density distributions in the space of genotypes are determined. It is shown that common viral evolutionary traits like diversification and extinction are driven by nonlocal interactions via immune responses, target-cell competition, and therapy. This provides us with a mechanistic explanation for clinically relevant properties like immune escape and drug resistance selection, and allows us to link virus genotypes to phenotypes.
中文翻译：
病毒进化的非局部反应扩散模型中菌株的存在与动力学
SIAM应用数学杂志，第81卷，第1期，第107-128页，2021年1月。
在这项工作中，我们建立了一个数学框架，用于预测和量化宿主生物感染过程中病毒多样性的演变。它被指定为相对于基因型和时间的病毒密度分布，该分布由反应扩散积分微分方程控制，其中考虑了病毒的突变，复制以及免疫细胞的消除和药物治疗。确定存在与基因型空间中的局部密度分布相对应的病毒株的条件。研究表明，常见的病毒进化特征（如多样化和灭绝）是由免疫反应，靶细胞竞争和治疗等非局部相互作用所驱动。这为我们提供了有关临床相关属性（例如免疫逃逸和药物抗性选择）的机械解释，
更新日期：2021-01-26
In this work, we develop a mathematical framework for predicting and quantifying virus diversity evolution during infection of a host organism. It is specified as a virus density distribution with respect to genotype and time governed by a reaction-diffusion integro-differential equation taking virus mutations, replication, and elimination by immune cells and medical treatment into account. Conditions for the existence of virus strains that correspond to localized density distributions in the space of genotypes are determined. It is shown that common viral evolutionary traits like diversification and extinction are driven by nonlocal interactions via immune responses, target-cell competition, and therapy. This provides us with a mechanistic explanation for clinically relevant properties like immune escape and drug resistance selection, and allows us to link virus genotypes to phenotypes.
中文翻译：
病毒进化的非局部反应扩散模型中菌株的存在与动力学
SIAM应用数学杂志，第81卷，第1期，第107-128页，2021年1月。
在这项工作中，我们建立了一个数学框架，用于预测和量化宿主生物感染过程中病毒多样性的演变。它被指定为相对于基因型和时间的病毒密度分布，该分布由反应扩散积分微分方程控制，其中考虑了病毒的突变，复制以及免疫细胞的消除和药物治疗。确定存在与基因型空间中的局部密度分布相对应的病毒株的条件。研究表明，常见的病毒进化特征（如多样化和灭绝）是由免疫反应，靶细胞竞争和治疗等非局部相互作用所驱动。这为我们提供了有关临床相关属性（例如免疫逃逸和药物抗性选择）的机械解释，
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