Department of Mathematics, Augusta University, Augusta, GA, United States of America.
PLoS One. 2022 Jul 29;17(7):e0271446. doi: 10.1371/journal.pone.0271446. eCollection 2022.
In this work, an innovative multi-strain SV EAIR epidemic model is developed for the study of the spread of a multi-strain infectious disease in a population infected by mutations of the disease. The population is assumed to be completely susceptible to n different variants of the disease, and those who are vaccinated and recovered from a specific strain k (k ≤ n) are immune to previous and present strains j = 1, 2, ⋯, k, but can still be infected by newer emerging strains j = k + 1, k + 2, ⋯, n. The model is designed to simulate the emergence and dissemination of viral strains. All the equilibrium points of the system are calculated and the conditions for existence and global stability of these points are investigated and used to answer the question as to whether it is possible for the population to have an endemic with more than one strain. An interesting result that shows that a strain with a reproduction number greater than one can still die out on the long run if a newer emerging strain has a greater reproduction number is verified numerically. The effect of vaccines on the population is also analyzed and a bound for the herd immunity threshold is calculated. The validity of the work done is verified through numerical simulations by applying the proposed model and strategy to analyze the multi-strains of the COVID-19 virus, in particular, the Delta and the Omicron variants, in the United State.
在这项工作中，开发了一种创新的多菌株 SV EAIR 传染病模型，用于研究人群中由疾病突变引起的多菌株传染病的传播。假设人群对 n 种不同变体的疾病完全易感，那些接种疫苗并从特定菌株 k（k ≤ n）中康复的人对以前和现在的菌株 j = 1、2、...、k 具有免疫力，但仍可能感染新出现的菌株 j = k + 1、k + 2、...、n。该模型旨在模拟病毒株的出现和传播。计算了系统的所有平衡点，并研究了这些点存在和全局稳定性的条件，并用于回答人群是否可能存在多种菌株流行的问题。通过数值验证了一个有趣的结果，即如果新出现的菌株具有更大的繁殖数，那么繁殖数大于 1 的菌株在长期内仍可能灭绝。还分析了疫苗对人群的影响，并计算了群体免疫阈值的上限。通过应用所提出的模型和策略来分析 COVID-19 病毒的多种菌株，特别是美国的 Delta 和 Omicron 变体，对所做工作的有效性进行了数值模拟验证。
