Gamma–distributed transmission memory in a reaction–diffusion epidemic model with nonlinear incidence

Martin Anokye, Luca Guerrini, John Amoah Mensah, Michael Fosu Ofori and Stefania Ragni

PLOS ONE, 2026, vol. 21, issue 10, 1-21

Abstract: We extend the delayed reaction–diffusion SI model with nonlinear incidence proposed by Song et al. by replacing the fixed transmission lag with weak and strong gamma-distributed memory kernels. Because the model has no exposed compartment, the memory term is interpreted phenomenologically as a distributed timing of transmission-related effects of past infectious states rather than as an explicit latent-stage mechanism. Using the same parameter set adopted by Song et al., we show that the distributed-memory models have a stability structure that is qualitatively different from that of the discrete-delay model. For the spatially homogeneous mode, both gamma kernels exhibit a small stabilising spectral Hopf crossing at a mean memory time near 0.08. The discrete-delay model has a comparable small stabilising crossing but, in addition, a much larger destabilising crossing near τ=1.335. Consequently, at the nominal values 1.2 and 1.6 used in the reference simulations, the gamma models converge to the selected endemic equilibrium, whereas the discrete-delay model crosses into an oscillatory regime. The first spatial mode is different: for the gamma formulations its modal constant term is negative for every positive memory rate, so this mode is unstable for every positive mean-memory value. We therefore interpret this behavior as a memory-independent spatial-mode instability, distinct from both a memory-induced Hopf crossing and a classical Turing instability.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0360508 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 60508&type=printable (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0360508

DOI: 10.1371/journal.pone.0360508

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().