Abstract
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’.
Highlights
Despite centuries of efforts to improve public health and mitigate epidemic disease effects, the threat of infectious diseases remains
When we consider the spread of an epidemic, it is the contact structure between individuals that determines the progress of the disease through the population
We have derived the basic reproduction number of the basic SIR model closed by probability-generating function (PGF)
Summary
Despite centuries of efforts to improve public health and mitigate epidemic disease effects, the threat of infectious diseases remains. Where R01 and R02 are the basic reproduction numbers of the SIR and SAR models, respectively, which are the expected numbers of secondary infections caused by a single-infected individual in a completely susceptible population if there is only one virus spreading in the network. Define R0 = max{R01, R02, (β + μ)Φξ /(α1 + α2)}, if R0 < 1, the disease-free equilibrium E0 of system (3.1) is locally stable; otherwise, it is unstable This shows clearly that, in the two-strain competing model, only controlling their own spreading thresholds is not enough. The value of (β + μ)Φξ /(α1 + α2) has a vital influence on the state of infection, that is to say, the spreading threshold of the two-strain competing model depends on the degree distribution, and is related to the clustering coefficient of the network
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
