| In the history of all times and all over the world,epidemics have profoundly affected the fate of mankind.The outbreak and spread of infectious diseases in history may directly or indirectly change the development process of a country or even an era.The outbreak of coronavirus disease 2019(COVID-19)in December 2019 brought great challenges to the economic development and health of human society.The research on mathematical modeling of epidemic transmission is of great significance and potential application value.More and more scientists use mathematical modeling methods to study the spread,early warning,and prevention and control situation of COVID-19 pandemic.With the rapid increase of COVID-19 confirmed cases,medical resources become tenser and tenser.The admission process for a large number of COVID-19 patients in medical institutions has also become increasingly difficult.For such a complex system,it is a very important issue to fully understand the internal relationship between the limited medical resources and the death toll of COVID-19 pandemic.On this basis,it has become an important challenge for the authorities to seek more effective admission policies to make full use of limited medical resources to minimize the number of deaths.Based on the dynamics of epidemic spread,the evolution process of the disease of patients with COVID-19,non-Markov process,and medical queuing system,this thesis focuses on how to quantitatively evaluate and effectively reduce the death toll of COVID-19 pandemic under limited medical resources.It can provide reference value for the study of this epidemic and the possible future pandemic.The main research work is as follows:First of all,this thesis integrates the information of the possible state of the COVID-19 patients,their transfer process,and the limited medical resources,and puts forward a non-Markov model: the COVID-19 patient admission model based on limited medical resources.According to the clinical statistics of patients,this thesis simulates the process of patients' admission in Wuhan and Lombardy,Italy.The model can accurately evaluate the change of local death toll with time.On this basis,the quantitative impact of the timing of medical resources deployment and the amount of resources input on the number of deaths and the pressure of the medical system is further discussed.Research shows that the lack of medical resources may lead to a surge in the number of deaths.Early deployment and/or increased medical resources will significantly reduce the number of deaths.Secondly,this thesis introduces the age factor,establishes an improved model based on the age structure,and studies the quantitative impact of selective Intensive Care Unit(ICU)admission strategy on the death toll for patients with COVID-19 in different age groups.The numerical simulation results of the improved model could fit the empirical mortality rate of patients of different ages well.This thesis further proposes a priority scheduling method for different age groups to find the optimal admission strategy of ICU.The results show that the number of deaths in Wuhan and Lombardy will be reduced by 10.4% and 6.7% respectively compared with the First Come-First Served(FCFS)strategy with the limited waiting time.Finally,this thesis quantitatively evaluates the implementation effect of a selective ICU treatment strategy based on age structure in different scenarios.Considering the differences in age structure and per capita medical resources of different countries and regions,we systematically discuss the performance of selective ICU admission strategy based on age structure in different scenarios.In this thesis,an optimized efficiency index was developed to evaluate the efficacy of selective ICU admission strategies implemented in different countries: China,Korea,Italy,and Spain.The results show that in countries with a younger population structure and fewer medical resources per capita,the selective ICU treatment strategy based on age structure has a good effect. |
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