A fractional stochastic SPEIQR epidemic model in switching network for COVID-19 ☆

The rapid spread of COVID-19 globally is the cause of panic and billions of dollars in losses and some public policies have been implemented to contain the spread of the virus. It is highly significant to establish mathematical models to describe the spread of the pandemic. In this paper, a fractional stochastic susceptible-protected-exposed-infected-quarantined-recovered (SPEIQR) epidemic model in switching network is proposed to investigate COVID-19 and other diseases in the future, in which the switching connections in the propagation network of viruses based on a Bernoulli random variable are given to represent the policy change during COVID-19. The effects of environmental fluctuations are also considered by introducing the multiplicative noise terms into the disease transmission coefficient to obtain a more realistic mathematical model. Furthermore, the Riemann-Liouville fractional derivative is used to describe the dynamics of disease transmission process which is dependent on the history information of the stochastic system. Some qualitative properties of the model are derived and some sufficient conditions are obtained to ensure the local extinction with probability one of the disease. Finally, we use the epidemic data of three countries (Italy, Germany and Switzerland) and three cities in China (Hubei, Hunan and Henan) from January 22 to July 20 to demonstrate the validity of the derived results and the availability of the proposed models. This work provides some theoretical results to deeply understand the dynamics of COVID-19 and regulate the disease dynamics.