Department of Physics, Humboldt-Universität zu Berlin, 12489, Berlin, Germany.
Potsdam Institute for Climate Impact Research (PIK), 14473, Potsdam, Germany.
Sci Rep. 2020 Apr 3;10(1):5919. doi: 10.1038/s41598-020-62597-5.
Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent's infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation.
传染病和许多病原体的进化通常发生在相似的时间尺度上，因此它们的动态往往交织在一起。在这里，作为理论研究这一问题的第一步，我们分析了在具有网格状连接的简单 SIR 网络上传播的突变病原体。我们考虑了传染病的空间方面，它通常沿着宿主或宿主群体（如城市或国家）之间的交通联系传播。我们关注的是增强病原体感染率的突变情况。我们发现，小世界特性（即长程连接的存在）使网络非常脆弱，支持频繁的超临界突变，并使网络从疾病灭绝转变为全面流行。然而，对于非常多的长程连接，效果会逆转，我们发现大规模爆发的机会减少。我们研究了两种情况，一种是具有离散突变步骤的情况，另一种是具有连续遗传变量的情况，并分析了各种标度律。对于连续情况，我们为概率密度导出了类似于福克-普朗克的方程，并使用 WKB 近似法对少数捷径进行了解析。我们的分析支持了这样的观点，即在传染病波期间可能会发生传播能力增强的突变，而不一定是在其开始之前。
