English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper provides a first attempt to incorporate the massive discontinuouschanges in the spatio-temporal dynamics of epidemics. Namely, we propose anextended class of epidemic models, governed by coupled stochastic semilinearpartial differential equations, driven by pure-jump L\'evy noise. Based on theconsidered type of incidence functions, by virtue of semi-group theory, atruncation technique and Banach fixed point theorem, we prove the existence andpathwise uniqueness of mild solutions, depending continuously on the initialdatum. Moreover, by means of a regularization technique, based on the resolventoperator, we acquire that mild solutions can be approximated by a suitableconverging sequence of strong solutions. With this result at hand, for positiveinitial states, we derive the almost-sure positiveness of the obtainedsolutions. Finally, we present the outcome of several numerical simulations, inorder to exhibit the effect of the considered type of stochastic noise, incomparison to Gaussian noise, which has been used in the previous literature.Our established results lay the ground-work for investigating other problemsassociated with the new proposed class of epidemic models, such as asymptoticbehavior analyses, optimal control as well as identification problems, whichprimarily rely on the existence and uniqueness of biologically feasiblesolutions.

Well-posedness results for a new class of stochastic spatio-temporal SIR-type models driven by proportional pure-jump L\'evy noise