Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A Study of Epidemiological Processes by Criticality Analysis
Hessam Hessami, Nicolas Glade

Last modified: 2014-03-31


Theoretical studies in epidemiology mainly use differential equations to study the infectious process of contagious diseases. The application of these formulations is a useful tool for the analytical study of epidemiological models. However an epidemic process that includes several aspects (e.g. biological, environmental, geographical, demographical or socio-cultural) in a differential system becomes complicated and mostly impossible to solve explicitly. The differential systems are poorly adapted to understand such phenomena at the microscopic level, i.e. at a fine-grain scale (individuals, small groups). These deterministic models are not even efficient at macroscopic levels (population scale) because of several unrealistic assumptions on which they are based. This points out the importance of studying epidemiological models in different ways. One is to treat them as natural critical phenomena (avalanches, earthquakes, species extinctions …) that result from series of stochastic processes that can be modeled at the microscopic scale.

Here, we aim to study the effect of socio-environmental factors on the dynamics of SIS and SIRS (Susceptible, Infected, Recovered immune individuals) models by using different simulation methods : Gillespie-based SSA (stochastic simulation algorithm) with homogeneous populations, SSA methods with the addition of group structures, and multi-agent simulation (MAS) with natural spatio-temporal dynamics. The two latter models bring the question of how social rules affect the formation of group structures and consequently influence the adequate number of contacts between individuals in the context of disease transmission. In the other hand, the nature and structure of human environments, the physical distances and distribution of individuals in a given society, but also the number of immune individuals (R) in population that, as natural barriers, play an important role in the spread of diseases. In our models, we will study the effect of these factors on the epidemic process dynamics. SSA and MAS models both provide fine-grain information: a microscopical resolution of time, space and population of epidemic processes. We propose here a new understanding of such processes based on self-organized criticality analysis.

Our goal is to extract the essence of real epidemiological systems and provide a new method for identifying a characteristic signature of different types of epidemic processes and of the factors that affect their dynamics. These signatures are identified according to the probability density distribution of macro-events (temporal contiguous microscopic events of contagion, of recovery ...) and their survival function. They might depend on model parameters such as infectious-recovery rates, vaccination strategies, spatial or social-cultural factors and provide more useful information than the synthetic thresholds which are conventionally used in epidemiology (e.g. R0). Then, we suggest the use of various methods based on computer studies such as participative simulation (a kind of MAS in which all or part of the agents are avatars of real people playing a role in a serious game) or the use of smart-phone technologies and social networks to yield big-data information and use them in simulation algorithm.


Epidemiology;Self-organized criticality;SSA (stochastic simulation algorithms);MAS (multi-agent simulation)