2018/06/15 by Rosanna C. Barnard, Luc Berthouze, Barnard, Rosanna C. +6 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #COVID-19 epidemiological studies #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE) #math.DS #physics.soc-ph #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1806.06135
arxiv created 2018/06/15 · openalex publication_date 2018/06/15 · arxiv updated 2018/06/19 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28
The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics the epidemic threshold is well studied and understood. However, it is less so for clustered networks where theoretical results are mostly limited to idealised networks. In this paper we focus on a class of models known as pairwise models where, to our knowledge, no analytical result for the epidemic threshold exists. We show that by exploiting the presence of fast variables and using some standard techniques from perturbation theory we are able to obtain the epidemic threshold analytically. We validate this new threshold by comparing it to the numerical solution of the full system. The agreement is found to be excellent over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. Interestingly, we find that the analytical form of R0 depends on the choice of closure, highlighting the importance of model choice when dealing with real-world epidemics. Nevertheless, we ex- pect that our method will extend to other systems in which fast variables are present.