A class of anomalous diffusion epidemic models based on CTRW and distributed delay  

作　　者：Zhenzhen Lu Guojian Ren Yangquan Chen Xiangyun Meng Yongguang Yu 

机构地区：[1]Department of Mathematics Beijing Jiaotong University Beijing 100044,P.R.China [2]Mechatronics,Embedded Systems and Automation Lab,University of California Merced,5200 North Lake Road Merced,CA 95343,USA

出　　处：《International Journal of Biomathematics》2023年第7期249-281,共33页生物数学学报（英文版）

基　　金：This work is supported in part by the National Natural Science Foundation of China(Grant Nos.62173027,62003026 and 61973329);the Natural Science Foundation of Beijing Municipality(Grant No.Z180005);Alianza UCMX seed funding(2020-2022)on Binational Collaborative Projects addressing COVID-19.

摘　　要：In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contrast to the traditional reaction-diffusion epidemic models.The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable.Specifically,based on the continuous-time random walk(CTRW),starting from two stochastic processes of the waiting time and the step length,time-fractional space-fractional diffusion,timefractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR(S:susceptible,I:infectious and R:recovered)epidemic models,respectively.The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays.Distributed time delay systems can also be reduced to existing models,such as the standard SIR model,the fractional infectivity model and others,within the proper bounds.Meanwhile,as an application of the above stochastic modeling method,the physical meaning of anomalous diffusion is also considered by taking the SEIR(E:exposed)epidemic model as an example.Similar methods can be used to build other types of epidemic models,including SIVRS(V:vaccine),SIQRS(Q:quarantined)and others.Finally,this paper describes the transmission of infectious disease in space using the real data of COVID-19.

关 键 词：Continuous-time random walk time-fractional space-fractional diffusion time-fractional reaction-diffusion fractional-order diffusion distributed time delay 

分 类 号：O175[理学—数学]