{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T05:17:23Z","timestamp":1778563043807,"version":"3.51.4"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barab\u00e1si\u2013Albert (BA), Erd\u00f6s\u2013R\u00e9nyi (ER), and Watts\u2013Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM&lt;R0. For RM,R0&gt;1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.<\/jats:p>","DOI":"10.3390\/e26050362","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T08:08:32Z","timestamp":1714032512000},"page":"362","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1123-1061","authenticated-orcid":false,"given":"T\u00e9o","family":"Granger","sequence":"first","affiliation":[{"name":"Sorbonne Universit\u00e9, Institut Jean le Rond d\u2019Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7955-6666","authenticated-orcid":false,"given":"Thomas M.","family":"Michelitsch","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Institut Jean le Rond d\u2019Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3152-8356","authenticated-orcid":false,"given":"Michael","family":"Bestehorn","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik, Brandenburgische Technische Universit\u00e4t Cottbus-Senftenberg, Erich-Weinert-Stra\u00dfe 1, 03046 Cottbus, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9243-3246","authenticated-orcid":false,"given":"Alejandro P.","family":"Riascos","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad Nacional de Colombia, Bogot\u00e1, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernard A.","family":"Collet","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Institut Jean le Rond d\u2019Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"key":"ref_1","unstructured":"Rhodes, P., and Bryant, J.H. 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