World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

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

    https://doi.org/10.1142/S1793524522501303Cited by:1 (Source: Crossref)

    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, time-fractional 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.


    Remember to check out the Most Cited Articles in IJB!
    Check out new Biomathematics books in our Mathematics 2018 catalogue!
    Featuring author Frederic Y M Wan and more!