Fuzzy Cellular Automata Model for Discrete Dynamical System Representing Spread of MERS and COVID-19 Virus

Abstract

Basu, Sumita Ghosh, SreeyaDynamical system is the mathematical model for computing changes over time of any physical, biological, economic or social phenomena. Usually discrete dynamical system is described mathematically by difference equations and the solution of such difference equation gives the exact value of the changing variable over time. Another widely used computation model that predicts the trend of the dynamical system is Cellular Automata. Crisp Cellular Automata model which makes use of exactly measurable variables and parameters have been studied widely. However, our practical experience tells us that getting exact measurement of any physical, biological, economic or social phenomena is difficult, if not impossible. The inexactness arising due to imprecision or vagueness is called fuzzy uncertainty and was introduced by Zadeh [22]. The discrete dynamical system where the measurements of variables and/or parameters are imprecisely defined are modelled by Fuzzy Difference Equations or Fuzzy Cellular Automata. We have found fuzzy triangular number solutions of fuzzy one dimensional first order finite difference equation and corresponding fuzzy cellular automata model. This technique have been used to find a fuzzy cellular automata model for the dynamical system representing MERS and COVID-19 virus spread. The model so obtained reveals the trend of growth and gradation of the infection.