The influence of immune individuals in disease spread evaluated by cellular automaton and genetic algorithm

Abstract

Background and objective: One of the main goals of epidemiological studies is to build models capable of forecasting the prevalence of a contagious disease, in order to propose public health policies for combating its propagation. Here, the aim is to evaluate the influence of immune individuals in the processes of contagion and recovery from varicella. This influence is usually neglected.

Methods: An epidemic model based on probabilistic cellular automaton is introduced. By using a genetic algorithm, the values of three parameters of this model are determined from data of prevalence of varicella in Belgium and Italy, in a pre-vaccination period.

Results: This methodology can predict the varicella prevalence (with average relative error of 2%-4%) in these two European countries. Belgium data can be explained by ignoring the role of immune individuals in the infection propagation; however, Italy data can be explained by considering contagion exclusively mediated by immune individuals.

Conclusions: The role of immune individuals should be accurately delineated in investigations on the dynamics of disease propagation. In addition, the proposed methodology can be adapted for evaluating, for instance, the role of asymptomatic carriers in the novel coronavirus spread.

Keywords: Cellular automaton; Contagious disease; Genetic algorithm; SIR model.

Fig. 1

Time evolutions of the percentages of S-individuals (solid line), I-individuals (dotted line), and R-individuals (dash-dotted line) from an initial condition with 99% of S-individuals and 1% of I-individuals (and, obviously, 0% of R-individuals), obtained from a numerical simulation of the CA model with $n=500,$$m=8,$$r=192,$$k=0.2,$$q=0.1,$$p=0.1,$$P_3=0.5,$$P_5=0.2,$and $P_6=0.2$. The systems reaches an endemic steady-state given by $S^{*}=0.31,$$I^{*}=0.18,$and $R^{*}=0.51$.

Fig. 2

Time evolution of the fitness by using F₁. The minimum, maximum, and average values of F₁ are shown for the 100 generations. In each generation, the maximum value corresponds to the best-fit chromosome, the minimum value to the worst-fit chromosome, and the average value is determined by taking into account the 100 chromosomes.

Fig. 3

Time evolution of the fitness along 100 generations by using F₂.

Fig. 4

Time evolution of the fitness along 100 generations by using F₃.