Contact Adaption During Epidemics: A Multilayer Network Formulation Approach

Abstract

People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among 2 N possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold-a characteristic measure of a contact network robustness against epidemics-in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.

An optimized SIR Modeling for Analyzing the Spreading Rate of Covid-19 Pandemic

“…Similarly, the derivative of the infected population is given in (2). It consists of the susceptible stage with birth rate and death rate respectively.…”

“…This virus is very infectious for the first three days once the virus has been confirmed to the individuals. Therefore, the Government are imposing lockdown and asking people wear the mask and maintain social distancing and quarantine etc., to contain the virus [2]. To detect the spreading rate mathematical modeling of virus spread is very essential.…”

On assessing control actions for epidemic models on temporal networks

“…An optimal control problem has been formulated for this model in [25]. A different implementation considers an adaptive scenario, in which alerted individuals change local contacts rather than adopting self-protective behaviors [26]. Preliminary results on the original SAIS models on ADNs can be found in [27], while the problem of cost-aware containment of epidemics is studied for the adaptive scenario in [28].…”

Classification of link-breaking and link-creation updating rules in susceptible-infected-susceptible epidemics on adaptive networks

“…One of the simplest, nontrivial dynamical processes on networks is the susceptibleinfected-susceptible (SIS) model [1]. Epidemic models like the SIS model describe a wide variety of diffusive processes, including epidemics [2,3], opinion spreading [4], computer viruses [5], brain data transfers [6], fake news spreading [7], failure propagation [8], and internet packet routing [9]. Most studies have either addressed the dynamics of the network or the dynamics on the network.…”