Periodic forcing in a three-level cellular automata model for a vector-transmitted disease

Abstract

The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time-series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of absence of external periodic drive, the model predicts completely distinct long time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided the forcing term takes into account the local rainfall modulation. Finally, the dependence between epidemics threshold and vector control undergoes a transition from power law to stretched exponential behavior due to human mobility effect.

Parameterization and Sensitivity Analysis of a Complex Simulation Model for Mosquito Population Dynamics, Dengue Transmission, and Their Control

“…These results are consistent with other modeling studies reporting the importance of mosquito survival or mortality, [14][15][16][17][18][19][20][21] biting rate, 6,14,15,17,18,22 and length of the infectious period in the host 6,14,21,[23][24][25][26][27] in determining the dynamics of mosquitoborne diseases. However, our results go one step further by identifying specific causes of mosquito mortality and the aspects of biting behaviors that may be most influential.…”

Modelling the dynamics of dengue real epidemics

“…In both epidemics, the population was naive for the circulating serotype. In a previous study some of us investigated the first epidemic (1995) using a cellular automata model (Santos et al 2009) forced by seasonal factors owing to the strong correlation between the weekly number of cases and the rainfall in the city. In that study, the epidemic time series were reproduced quantitatively as well as their qualitative time-spatial patterns, and preliminary investigations were carried out on vector control throughout the model.…”

A Cellular Automata Modeling for Visualizing and Predicting Spreading Patterns of Dengue Fever

“…Moreover, the rule of neighborhood in determining the model interactions was described in [11]. The other important aspect that determines the accuracy of CA model is the transmition rule f. This rule was able to be represented as a deterministic or probabilistic function [9][10]. Many methods to find function f as rule of the CA model have been introduced such as using Markov Chain [12], the differential equations of the classical model [13], and the Genetic Algorithm [14].…”

“…Some studies have been conducted such as developing a mathematical model of disease spread and its simulation using Cellular Automata (CA) [6], analyzing some scenarios of disease spread [7], applying the CA approach to the Susceptible-Infective-Recovered (SIR) model of disease spread by considering birth and death factors and the changes of rules for each state in the dynamic CA [8], and analyzing the complex spatiotemporal patterns observed in transmission of vector infectious disease [9].…”