Epidemic spread with asymptomatic infectious period in contact adaptive networks.

Abstract

We model an epidemic spread process involving nodes that (a) experience non-trivial asymptomatic infectious periods and (b) adapt by avoiding contacts with symptomatic infectious nodes. These modeling choices reflect ample evidence that infectious individuals are often mistakenly perceived as safe contacts due to lack of symptoms and that individuals adapt to an epidemic by avoiding contacts deemed to be of risk. We capture these choices in the SIa Is S (Susceptible-Asymptomatic InfectedSymptomatic Infected-Susceptible) model, where we explicitly distinguish between asymptomatic and symptomatic infectious individuals. We adopt an individual-based mean-field epidemic modeling approach and formulate the system of differential equations via continuous-time Markov chain analysis. We first consider non-adaptive homogeneous and heterogeneous mixing scenarios over arbitrary static contact networks. We derive the expression for the basic reproduction number, R0, and establish that under otherwise similar conditions the individual infection probabilities at the metastable state of SIa Is S dominate those in the conventional SIS model. Then, we focus on a contact-adaptive setting, where nodes avoid interactions with known infectious neighbors or reconnect with neighbors who have recovered, to study how the time-varying contact network, asymptomatic infections and their combinations affect the epidemic spread dynamics. Overall, asymptomatic infections restrict nodes’ capacity to adapt (link breaking), resulting in higher link density and consequently higher epidemic prevalence. Besides, in their presence, the retarding effect of the link-breaking mechanism on epidemic prevalence is considerably mitigated. We numerically analyze how the effective link-breaking rate and the size of the asymptomatically infected population affect the link density and, ultimately, the epidemic prevalence. Furthermore, the epidemic threshold appears to scale inversely with the population of asymptomatic nodes, namely the epidemic starts to spread at lower infection rates when the number of asymptomatic infections is higher.