Markovian approach to tackle competing pathogens in simplicial complex

Abstract

Recent studies on network spreading dynamics often adopt pairwise interaction to describe the simple spreading process while using higher-order interaction to describe the collective behavior of the dynamical system on the network. However, the interaction between competing pathogens usually includes both pairwise and high-order interactions. Due to dynamic correlation, it is hard to solve the theory by considering two modes of interaction. Here, we propose a theoretical analysis framework based on Microscopic Markov Chain Approach (MMCA) to solve simplicial competing spreading involving pairwise and high-order interactions. Because of the competitive mechanism in the framework, a susceptible node can only be infected by one pathogen, and contagion can spread simultaneously through pairwise interactions (1-simplices) and higher-order interactions, i.e., 2-simplices. The theory and simulation agree in good accuracy on real networks and artificial networks, which reveals the validity of the theoretical analysis and indicates that the initial density of the two pathogens and the infection rate of 1-simplices act together on the process of pathogen transmission. The effect of 1-simplices and 2-simplices infection rates of two pathogens are also included in the discussion. When the average degree of the network is fixed, in the case of a larger average number of 1-simplices incidents on a node, infection rates of pathogen A is greater than infection rates of pathogen B may result in final infection density of pathogen A greater than the final infection density of pathogen B. We discuss the influences of 1-simplices average degree and 2-simplices average degree on the final infection range. We find that with the increase of 1-simplices average degree, the pathogen may undergo a transition from outbreak to death while increasing the 2-simplices average degree is more conducive to spreading. Finally, in the study of two different seed selection strategies, we find that selecting the nodes with the highest degree as seeds can promote pathogen spreading more than randomly selecting seeds.