Epidemionics: From the host-host interactions to the systematic analysis of the emergent macroscopic dynamics of epidemic networks

Abstract

One of the most critical issues in epidemiology revolves around the bridging of the diverse space and time scales stretching from the microscopic scale, where detailed knowledge on the immune mechanisms, host-microbe and host-host interactions is often available, to the macroscopic population-scale where the epidemic emerges, the questions arise and the answers are required. In this paper we show how the so called Equation-Free approach, a novel computational framework for multi-scale analysis, can be exploited to efficiently analyze the macroscopic emergent behavior of complex epidemic models on certain type of networks by acting directly on the multi-scale simulation. The methodology can be used to bypass the need of derivation of closures for the emergent population-level equations providing a systematic computational strict approach for macroscopic-level analysis. We illustrate the methodology through a stochastic individual-based model with agents acting on two different networks: a random regular and an Erdős-Rényi network. We construct the macroscopic bifurcation diagrams and locate the critical points that mark the onset of emergent hysteresis behavior which are associated with disease outbreaks. Finally, we perform a rare-events analysis that may in principle be used to estimate the mean time of possible outbreaks of phenomenologically latent infectious diseases.

Mathematical modeling of infectious disease dynamics

“…However, such simple simulations are inefficient for the systematic analysis of the emergent epidemic in the parameter space. New rigorous computational methodologies, such as the equation-free multiscale framework, 96,[139][140][141][142] that can be used to address this issue have the potential to expedite novel computational modeling and analysis as well as to enhance our understanding and forecasting capability to combat epidemic outbreaks.…”

Network epidemiology and plant trade networks

“…Despite the growing sophistications, spatial models of epidemics in networks are still simplifications of a complicated system (Reppas et al 2010). Only rarely is this acknowledged in the discussion of papers reporting results from models of epidemics in spatial networks, so that there is a danger of take-home messages being read without keeping in mind all the various caveats and assumptions of the mathematical models behind policy recommendations (Ferguson et al 2006; Fraser et al 2009; Garnett et al 2011).…”

Randomness switches the dynamics in a biophysical model for Parkinson Disease

“…The complication arises due to the following reasons: (a) the nonlinear, stochastic atomistic rules of the individuals units, (b) the coupling which usually has a complex network structure and (c) the multi-scale nature which emerges when one tries to bridge the micro-macro behavior. Complexity characterizes the behavior of many real-world systems; from gene to proteins and molecular interaction [1,2], from individual flu illness to epidemic spreading, forest fire spreading [3,4] and earthquakes occurrence [5,6]. The brain with about 12 10 neurons and 15 10 neurons interconnections with several tasks to execute such as, recognizing patterns (schemes, colors, odors), controlling movements, memorizing thinks, creating and solving problems, is often called the most complex system.…”