{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:54:12Z","timestamp":1760241252881,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,31]],"date-time":"2019-12-31T00:00:00Z","timestamp":1577750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004530","name":"Universiti Putra Malaysia","doi-asserted-by":"publisher","award":["GP-IPS\/2018\/9657400"],"award-info":[{"award-number":["GP-IPS\/2018\/9657400"]}],"id":[{"id":"10.13039\/501100004530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis. Therefore, we studied two susceptible classes      S 1   ( t )      and      S 2   ( t )     , each of which can be infected when interacting with two different infectious groups      I 1   ( t )      and      I 2   ( t )     . The stochastic models were formulated through the continuous time Markov chain (CTMC) along with their deterministic analogues. The statistics for the developed model were studied using the multi-type branching process. Since each epidemic class was assumed to transmit only its own type of pathogen, two reproduction numbers were obtained, in addition to the probability-generating functions of offspring. Thus, these, together with the mean number of infections, were used to estimate the probability of extinction. The initial population of infectious classes can influence their probability of extinction. Understanding the disease extinctions and outbreaks could result in rapid intervention by the management for effective control measures.<\/jats:p>","DOI":"10.3390\/e22010054","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T03:28:53Z","timestamp":1578022133000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8724-3758","authenticated-orcid":false,"given":"Auwal","family":"Abdullahi","sequence":"first","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"},{"name":"Department of Mathematics and Computer Science, Federal University Kashere, Kashere 771103, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0591-6627","authenticated-orcid":false,"given":"Shamarina","family":"Shohaimi","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"},{"name":"Department of Biology, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1217-963X","authenticated-orcid":false,"given":"Adem","family":"Kilicman","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"},{"name":"Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohd","family":"Hafiz Ibrahim","sequence":"additional","affiliation":[{"name":"Department of Biology, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nader","family":"Salari","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, School of Public Health, Kermanshah University of Medical Sciences, 6715847141 Kermanshah, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7039","DOI":"10.1073\/pnas.1501598112","article-title":"Rodent reservoirs of future zoonotic diseases","volume":"112","author":"Han","year":"2015","journal-title":"Proc. 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