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Philos Trans A Math Phys Eng Sci. 2017 Jun 28;375(2096). pii: 20160284. doi: 10.1098/rsta.2016.0284.

Spread of competing viruses on heterogeneous networks.

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Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.
College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, People's Republic of China.
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China


In this paper, we propose a model where two strains compete with each other at the expense of common susceptible individuals on heterogeneous networks by using pair-wise approximation closed by the probability-generating function (PGF). All of the strains obey the susceptible-infected-recovered (SIR) mechanism. From a special perspective, we first study the dynamical behaviour of an SIR model closed by the PGF, and obtain the basic reproduction number via two methods. Then we build a model to study the spreading dynamics of competing viruses and discuss the conditions for the local stability of equilibria, which is different from the condition obtained by using the heterogeneous mean-field approach. Finally, we perform numerical simulations on Barabási-Albert networks to complement our theoretical research, and show some dynamical properties of the model with competing viruses.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.


competing viruses; epidemic threshold; pair-wise; the basic reproduction number

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