Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach

Abstract

Background: The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic.

Methods: An epidemic is characterized trough an individual-based-model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies.

Results: A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease.

Conclusions: The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area play a central role in the dynamics of the desease.

Figure 1

Epidemic evolution for a large and completely homogeneous population. In figure we can see in blue real data; black line corresponds to automata model result and red to ODE based model.

Figure 2

Effect of initial spatial distributions for infected individuals.

Figure 3

Dynamics for high concentration spatial distribution and uniform concentration spatial distribution and low density.

Figure 4

Vaccination effect in disease dynamics for diffrerent vacinnated population size.

Figure 5

Effect of quarantine on the dynamics of the disease; (a) quarantine at a high population density; (b) quarantine at a low density population.