Cooperative coinfection dynamics on clustered networks

Peter Mann, V. Anne Smith, John B. O. Mitchell, and Simon Dobson

Phys. Rev. E 103, 042307 – Published 9 April 2021

Abstract

Coinfection is the process by which a host that is infected with a pathogen becomes infected by a second pathogen at a later point in time. An immunosuppressant host response to a primary disease can facilitate spreading of a subsequent emergent pathogen among the population. Social contact patterns within the substrate populace can be modeled using complex networks and it has been shown that contact patterns vastly influence the emergent disease dynamics. In this paper, we consider the effect of contact clustering on the coinfection dynamics of two pathogens spreading over a network. We use the generating function formulation to describe the expected outbreak sizes of each pathogen and numerically study the threshold criteria that permit the coexistence of each strain among the network. We find that the effects of clustering on the levels of coinfection are governed by the details of the contact topology.

Received 16 December 2020
Accepted 19 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042307

Physics Subject Headings (PhySH)

Cascades Clustering Continuous phase transition Cycles Degree distributions Epidemic Network structure Percolation phase transition Spreading

Erdos-Renyi graph Poisson degree distribution networks Random graphs Tree network Triangular network

Percolation theory

Networks

Authors & Affiliations

Peter Mann ^*, V. Anne Smith , John B. O. Mitchell , and Simon Dobson

School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, United Kingdom; School of Chemistry, University of St Andrews, St Andrews, Fife KY16 9ST, United Kingdom; and School of Biology, University of St Andrews, St Andrews, Fife KY16 9TH, United Kingdom

^*pm78@st-andrews.ac.uk

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Vol. 103, Iss. 4 — April 2021

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Images

Figure 1
The treelike edge topologies found in the GCC following the first strain and their probabilities.
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Figure 2
The 3-cycle edge topologies found in the GCC following the first strain and their probabilities. Node colors and patterns are defined according to Fig. 1. Triangles D, E, and F consist of inhomogeneous neighbor states and hence, due to the symmetry of the shape, their reflection about a vertical axis bisecting the focal node can also occur with equal probability. The curved arrows in triangles D and F indicate the additional pathway through the cycle by which the infected neighbor could infect the focal node.
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Figure 3
The outbreak fractions for the 2-strain coinfection model on doubly Poisson random graphs with $T_{2} = 0.6, N = 25 000$ , for varying clustering coefficients and fixed mean degree $〈 s 〉 + 2 〈 t 〉 = 2$ . It is clear that clustering reduces the epidemic thresholds of both diseases and reduces the outbreak size of the first strain; however, it increases the coinfected fraction of the network. Points are the average of 500 repeats of Monte Carlo simulation while solid lines are the theoretical predictions from Eqs. (14) and (15).
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Figure 4
An analytical investigation of the critical transmissibilities of both strains for increasing clustering coefficients for the doubly Poisson networks defined in Fig. 3. The curves are generated from Eqs. (14) and (15) at the value of $T$ in which the outbreak fraction becomes larger than $ε$ . The critical points reduce as $C$ increases, indicating that contact clustering helps to spread an emergent epidemic. The interval $[T_{1}^{*}, T_{2}^{*}]$ is the transmissibility window in which strain 1 exists as an epidemic on the network without strain 2. We observe that increased clustering reduces the interval and thus increases the extent of coinfection in this model, at the expense of the monoinfection equilibrium. We note, however, that clustering can never reduce the coinfection critical point below the single strain threshold due to the strict conditions of perfect coinfection in the premise of the model.
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Figure 5
Top: The outbreak fractions of both strains for increasing triangle probabilities within the CHCN degree distribution defined in Eq. (22). Clustering reduces the epidemic threshold, in agreement with Poisson graph experiments; however, coinfection decreases with increasing $θ$ . Bottom: The expected epidemic sizes of both strains for a $p^{CHCN} (k)$ network with $θ = 0.0$ and a degree- $δ$ CHCN distribution network defined by Eq. (24). Clustering increases the epidemic threshold in this model. Markers are the average of 100 repetitions of bond percolation on CHCN networks with $N = 1 e^{5}$ nodes and $T_{2} = 0.6$ .
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