论文标题
突变使大流行病变得更糟或更高：对SARS-COV-2变体进行建模和不完善的疫苗接种
Mutations make pandemics worse or better: modeling SARS-CoV-2 variants and imperfect vaccination
论文作者
论文摘要
自2020年12月以来，Covid-19（尤其是Delta和Omicron）的变体具有不同的特征，影响了世界各地的死亡和可传染性。为了解决该疾病的新动力学，我们提出了两个菌株的动力学模型，即天然和突变体，具有突变和不完善的疫苗接种动力学。还假定，来自天然应变的恢复个体可以通过与个体或受污染的表面或气溶胶的直接接触来感染突变株。我们独立计算每个应变的基本繁殖号，并以$ r_0 $的价格获得最大值。当基本繁殖数$ r_0 <1时，我们证明了使用中心歧管理论和无疾病平衡的全球稳定性证明向后分叉的不存在。中间突变率$ν_1$导致振荡。当$ν_1$在阈值中增加时，系统会重新获得其稳定性，并表现出一种有趣的动力学，称为Epentic Bubble。得出了疫苗诱导的牛群免疫力的分析表达。使用MCMC方法从3月1日至9月27日的9月27日，使用印度证实案件的累积数量和COVID-19死亡的累积数量的印度数据进行参数化。可以通过增加疫苗和突变菌株的疫苗功效来减少累积病例和死亡。我们观察到，通过将疫苗对天然应变的疗效为90 \％，累积病例和死亡将分别降低3.27 \％和5.2 \％。通过将疫苗对突变株的疗效为90 \％，累积病例和死亡将分别降低0.9 \％和2.5 \％。我们的研究表明，由于某些突变速率的振荡发生振荡，因此COVID-19的大流行可能会更糟，但由于在较低的感染水平下的稳定性和较大的突变速率，因此较高。
Since December 2020, variants of COVID-19 (especially Delta and Omicron) appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number for each strain independently and take the maximum for $R_0$. We prove the nonexistence of backward bifurcation using the center manifold theory, and global stability of disease-free equilibrium when the basic reproduction number $R_0<1. An intermediate mutation rate $ν_1$ leads to oscillations. When $ν_1$ increases over a threshold, the system regains its stability and exhibits an interesting dynamics called endemic bubble. An analytical expression for vaccine-induced herd immunity is derived. The model is parameterized using the Indian data of the cumulative number of confirmed cases and deaths of COVID-19 from March 1 to September 27 in 2021, using MCMC method. The cumulative cases and deaths can be reduced by increasing the vaccine efficacies to both native and mutant strains. We observe that by considering the vaccine efficacy to native strain as 90\%, the cumulative cases and deaths would be reduced by 3.27\% and 5.2\%, respectively; and by considering the vaccine efficacy to mutant strain as 90\%, the cumulative cases and deaths would be reduced by 0.9\% and 2.5\%, respectively. Our study demonstrates that the COVID-19 pandemic may be worse due to the occurrence of oscillations for certain mutation rates but better due to stability at a lower infection level with a larger mutation rate.
