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Article

Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities

1
Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2
Department of Mathematics and Computer Science, Federal University Kashere, Kashere 771103, Nigeria
3
Department of Biology, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
4
Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
5
Department of Biostatistics, School of Public Health, Kermanshah University of Medical Sciences, 6715847141 Kermanshah, Iran
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 54; https://doi.org/10.3390/e22010054
Received: 21 October 2019 / Revised: 15 November 2019 / Accepted: 21 November 2019 / Published: 31 December 2019
(This article belongs to the Special Issue From Time Series to Stochastic Dynamic Models)
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. View Full-Text
Keywords: branching process; continuous time Markov chain; epidemic extinction; Gillespie algorithm; basic reproduction number; stochastic differential equation branching process; continuous time Markov chain; epidemic extinction; Gillespie algorithm; basic reproduction number; stochastic differential equation
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MDPI and ACS Style

Abdullahi, A.; Shohaimi, S.; Kilicman, A.; Hafiz Ibrahim, M.; Salari, N. Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities. Entropy 2020, 22, 54. https://doi.org/10.3390/e22010054

AMA Style

Abdullahi A, Shohaimi S, Kilicman A, Hafiz Ibrahim M, Salari N. Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities. Entropy. 2020; 22(1):54. https://doi.org/10.3390/e22010054

Chicago/Turabian Style

Abdullahi, Auwal, Shamarina Shohaimi, Adem Kilicman, Mohd Hafiz Ibrahim, and Nader Salari. 2020. "Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities" Entropy 22, no. 1: 54. https://doi.org/10.3390/e22010054

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