RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different fitness distributions representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called lethal mutagenesis and mutational meltdown. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.
From viral evolution to spatial contagion: a biologically modulated Hawkes model
突变有时会增加进化中的病原体的传染性。在流行病期间，科学家利用病毒基因组数据推断出一个共同的进化历史，并将这一历史与地理传播联系起来。我们提出了一个直接将病原体的进化与其空间传染动力学联系起来的模型-有效地结合了系统发育推断和自激过程建模的两种流行病学范式-并将此\emph{phylogenetic Hawkes process}应用于2014-2016年西非埃博拉疫情的23，422例病毒病例的贝叶斯分析。所提出的模型能够检测到单个病毒，其时空传播速率显着提高，用于提供基因组数据的1，610个样本的子集。最后，为了促进大数据环境中的模型应用，我们开发了对数似然的梯度和Hessian的大规模并行实现，并在自适应预处理的Hamilton Monte Carlo例程中应用我们的高性能计算框架。
Viral Evolution and Adaptation as a Multivariate Branching Process
在本工作中，我们分析了RNA病毒群体的适应和进化问题，通过将基本随机模型定义为与Demetrius、Schuster和Sigmund在他们的多核苷酸进化研究中提出的分支过程密切相关的多变量分支过程（“Polynucleotide evolution and branching processes”，Bull.Math.Biol.46（1985）239-262）。我们表明，在没有有利的力量的模型是完全可解的。因此，有可能证明与这些系统的已知典型性质直接相关的几个关键结果，如（i）在分支过程理论的背景下，Bull，Sanjuán和Wilke提出的致死突变标准的证明（“Theory of lethal mutagenesis for viruses”，J. Virology 18（2007）2930-2939）;（ii）关于弛豫时间概念的新建议，并对其进行定量评价;在四个不同的制度：瞬态，“稳定”的平衡，灭绝阈值和致死突变的预期值的演变的定量描述。此外，可以预见对病毒种群演变动态的新见解。
Inferring infectiousness: a joint model of the within-host viral kinetics of SARS-CoV-2
Cleveland Clinic（克利夫兰诊所）；Cleveland Clinic Lerner College of Medicine of Case Western Reserve University（凯斯西储大学克利夫兰诊所勒纳医学院）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Colorado School of Public Health（科罗拉多公共卫生学院）；Imperial College London（伦敦帝国理工学院）；Stanford University（斯坦福大学）
Modeling Spatial Synchronization of Predator-Prey Oscillations via the XY Model under Demographic Stochasticity and Migration
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆理论物理国际中心）
