Study On The COVID-19 Transmission Dynamics Based On Isolation Delays And Multi-scale Nested Model

The COVID-19 pandemic in the worldwide poses an enormous threat to human health and bring huge challenges to public health,economic development,employment and other fields.Although the pathogenicity of the novel coronavirus is decreasing,its impact still cannot be ignored.How to deal with new infectious diseases in the present and future is still a big problem that deserves our attention.This paper mainly studies the transmission mechanism of COVID-19 infection from two perspectives,a transmission model of COVID-19 considering vaccination and isolation delays and a multi-scale model with infection age structure are constructed respectively,and their dynamic behaviors are studied and numerically simulated respectively.This paper is arranged as follows:Firstly,we construct a delay differential equation model to describe the transmission of COVID-19 on a macro scale,taking into account vaccination and isolation delays.According to the model,the basic reproduction number is obtained and the global dynamic analysis is carried out.According to the data of some real confirmed cases in Xi’an,the model parameters are estimated and the data are fitted.Then the partial rank correlation coefficients(PRCCs)and extened fourier amplitude sensitivity test(e FAST)are used for sensitivity analysis.The results show that the vaccination rate,vaccine effectiveness and the isolation rates of infected people had a significant impact on the control of the spread of COVID-19.In order to balance the economic loss caused by the epidemic,we consider an optimal control problem and obtain the optimal control strategy to minimize the number of infected individuals and the economic loss.Secondly,in order to investigate the effect of within-host virus dynamics on the betweenhost epidemiology dynamics,from the micro point of view,we nest the virus dynamics model into a macro transmission model of COVID-19,link the viral load to an individual’s infectivity in the population,and put forward a multi-stage and multi-scale nested transmission model of COVID-19 with infection age structure.We calculate the basic reproduction number and equilibria,analyze the global dynamics behavior of the nested model,and carry out the numerical simulation of the dynamics.Based on the Latin Hypercube sampling method,we perform sensitivity analysis by calculating PRCCs.Our results indicate that the transmission,replication and clearance of viruses within the host have significantly effect on the between-host system.Additionally,we consider administering drug therapy to individuals,our results suggest that the spread of the disease can be better controlled only when the effectiveness of the drug is stronger,otherwise it will prolong the infectious stage of the individual and the whole epidemic period.Lastly,we summarize the content and shortcomings of this paper,and give some ideas of the future research work.