Epidemic Spread Modeling with Time Variant Infective Population Using Pushdown Cellular Automata

The world without a disease is a dream of any human being. The disease spread if not controlled could cause an epidemic situation to spread and lead to pandemic. To control an epidemic we need to understand the nature of its spread and the epidemic spread model helps us in achieving this. Here we propose an epidemic spread model which considers not only the current infective population around the population but also the infective population which remain from the previous generations for computing the next generation infected individuals. A pushdown cellular automata model which is an enhanced version of cellular automata by adding a stack component is being used to model the epidemic spread and the model is validated by the real time data of H1N1 epidemic in Abu Dhabi. 1. Introduction Computational models in epidemics provide insight into dynamics of the disease spread across a geographical region. Given a small amount of relevant real time data the model would give us after certain amount of time what would be the epidemic situation across the geographical region. Cellular automata (CA) models are considered to be very handy and efficient in handling the real time simulation problems in epidemiology. The reason behind the simplicity of this CA model is its ability to attain the global behavior from the local behavior by the interaction of its cells [1–3]. The power of CA has been utilized to solve wide variety of problems like solving Weyl, Dirac, and Maxwell equations [4], diffusion equation [5], and Poisson equations [6]. Epidemic spread modeling through cellular automata has been an importance to many of the researchers. An efficient epidemic spread model through CA is given by Hoya White et al. [7]; in this model the population is assumed to be constant and the rules for the CA are considered to be static. The movement of population and its effects during an epidemic spread are given by Sirakoulis et al. [8]. The population when grouped under patches and their movement during an epidemic spread are discussed in our earlier work [9]. The spatial pattern and its dynamics along with noise in epidemics are being provided by Sun et al. [10]. Stochastic model for epidemic spread with quarantine and vaccination strategies have been provided by Wang Jeffrey [11]. In all these works discussed above, the susceptible population is infected by the infected population available in the current time step. There are no considerations for the populations who are infected at the previous time steps. If we consider the infected population at current time as , then