Gromov Dmitry, Romero-Severson Ethan O
Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, St. Petersburg 199034, Russia.
Department of Mathematics, National Research University Higher School of Economics, St. Petersburg Campus 16 Soyuza Pechatnikov Str., St Petersburg 190121, Russia.
Mathematics (Basel). 2020 Sep;8(9). doi: 10.3390/math8091500. Epub 2020 Sep 4.
Chronic viral infections can persist for decades spanning thousands of viral generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose an expandable mathematical framework for understanding how the emergence of genetic and phenotypic diversity affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. Our frameworks allows both neutral and phenotypic evolution, and we consider the specific evolution of contagiousness, resistance to therapy, and efficacy of prophylaxis. We compute both the controlled and uncontrolled, population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. We used these results to discuss the conditions under which the relative efficacy of prophylactic versus therapeutic methods of control are superior. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data.
慢性病毒感染可绵延数十年,历经数千代病毒繁衍,从而产生高度多样化的病毒群体,且有着自身复杂的进化史。我们提出了一个可扩展的数学框架,以理解遗传和表型多样性的出现如何通过非治愈性治疗和化学预防措施影响这些感染在群体水平上的控制。我们的框架允许中性和表型进化,并且我们考虑传染性、对治疗的抗性以及预防效果的具体进化情况。我们计算了考虑宿主内进化过程(新表型在感染者中出现和消失)的受控制和不受控制的群体水平基本再生数,我们还将其扩展以纳入治疗和预防控制措施。我们利用这些结果讨论了预防与治疗控制方法的相对疗效更优的条件。最后,对于宿主内进化模型的某些受限版本,我们给出了这些模型的地方病平衡点的表达式,为从群体水平遗传序列数据估计宿主内进化参数提供了一种潜在方法。