Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia.
College of Science and Engineering, James Cook University, Townsville, Australia.
Math Biosci. 2018 Feb;296:82-92. doi: 10.1016/j.mbs.2017.12.006. Epub 2017 Dec 27.
We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains - even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning.
我们介绍并分析了耦合的多菌株传染病模型，旨在模拟突变（如耐药性）病原体菌株的出现和传播。特别是，我们研究了一类一般的多菌株传染病模型的数学和生物学特性，其中每个菌株的感染舱以一般的方式耦合在一起。我们推导出了每个菌株的基本繁殖数的显式表达式，并强调了它们在调节系统动力学（例如传染病爆发的可能性）和非负地方病解的存在方面的重要性。重要的是，我们发现每个菌株的基本繁殖数与菌株之间的突变率无关——即使在感染舱耦合形式的相当一般的假设下也是如此。此外，我们验证了耦合项促进了菌株共存（作为竞争排除原理的扩展），并表明繁殖能力最强的菌株不一定是最流行的。最后，我们简要讨论了我们的结果对公共卫生政策和规划的意义。
