MODELING AND SIMULATION (Optional Paper)

Introduction to modeling and simulation, Definition of System, Type of System: Discrete system and continuous system, classification of systems, Modeling process, Advantage and disadvantage of simulation, Classification and limitations of mathematical models and its relation to simulation.

Modeling through differential equation: Linear growth and decay models, Nonlinear growth and decay models, Logistic model, Basic model relevant to population dynamics (Prey-Predator model, Competition model), Volterra’s principle.

Compartment models:  One-Compartment models and Two-Compartment models, Equilibrium solution, Stability analysis, Model validity and verification of models (Model V&V), Modeling through graph (in terms of weighted graph, In terms of signed graph, in terms of directed Graph).

Mathematical modeling through ordinary differential equation: SI model, SIR model with and without vaccination. Partial differential equation: Mass and momentum balance equations, wave equation.

Basic concepts of simulation languages, Overview of numerical methods used for continuous simulation, Stochastic Process (Marcov process, Transition probability, Marcov chain, Steady state condition, Marcov analysis), Discrete system simulation (Monte Carlo method, Random number generation).