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Register a new userBeyond network structure: How heterogenous susceptibility modulates the spread of epidemics
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The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that--for the SIS model--differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a nodes degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.
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Infectious diseases are a significant threat to human society which was over sighted before the incidence of COVID-19, although according to the report of the World Health Organisation (WHO) about 4.2 million people die annually due to infectious disease. Due to recent COVID-19 pandemic, more than 2 million people died during 2020 and 96.2 million people got affected by this devastating disease. Recent research shows that applying individual interactions and movements data could help managing the pandemic though modelling the spread of infectious diseases on social contact networks. Infectious disease spreading can be explained with the theories and methods of diffusion processes where a dynamic phenomena evolves on networked systems. In the modelling of diffusion process, it is assumed that contagious items spread out in the networked system through the inter-node interactions. This resembles spreading of infectious virus, e.g. spread of COVID-19, within a population through individual social interactions. The evolution behaviours of the diffusion process are strongly influenced by the characteristics of the underlying system and the mechanism of the diffusion process itself. Thus, spreading of infectious disease can be explained how people interact with each other and by the characteristics of the disease itself. This paper presenters the relevant theories and methodologies of diffusion process that can be used to model the spread of infectious diseases.
We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the ``choosiness`` exercised during pair-formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair-formation. By iterating over model mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.
Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations, and may bounce back to its original state, which is considered resilient. Here, we study the resilience of epidemics on networks, by introducing a different infection rate ${lambda_{2}}$ during SIS (susceptible-infected-susceptible) epidemic propagation to model perturbations (control state), whereas the infection rate is ${lambda_{1}}$ in the rest of time. Through simulations and theoretical analysis, we find that even for ${lambda_{2}<lambda_{c}}$, epidemics eventually could bounce back if control duration is below a threshold. This critical control time for epidemic resilience, i.e., ${cd_{max}}$ can be predicted by the diameter (${d}$) of the underlying network, with the quantitative relation ${cd_{max}sim d^{alpha}}$. Our findings can help to design a better mitigation strategy for epidemics.
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well-suited for estimation by distributed simulation. We describe a collection of graphs derived from ErdH{o}s-Renyi and scale-free-like random graphs in which we have manipulated assortativity-by-degree and the number of triangles. We evaluate the network reliability for all these graphs under a reliability rule that is related to the expected size of a connected component. Through these extensive simulations, we show that for positively or neutrally assortative graphs, swapping edges to increase the number of triangles does not increase the network reliability. Also, positively assortative graphs are more reliable than neutral or disassortative graphs with the same number of edges. Moreover, we show the combined effect of both assortativity-by-degree and the presence of triangles on the critical point and the size of the smallest subgraph that is reliable.
In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDEs), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compute a new R0-like threshold quantity and an implicit analytical relation between this and the final epidemic size. In addition we show that the pairwise model and the analytic calculations can be generalized in terms of integro-differential equations to any distribution of the infectious period, and we illustrate this by presenting a closed form expression for the final epidemic size. By showing the rigorous mathematical link between non-Markovian network epidemics and pairwise DDEs, we provide the framework for a deeper and more rigorous understanding of the impact of non-Markovian dynamics with explicit results for final epidemic size and threshold quantities.
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