MODELING AND SIMULATION (Optional Paper)
This course will enable the students to -
- Provide knowledge about Modeling and Simulation (M & amp; S) which is the use for different models (e.g., physical, mathematical, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making.
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Learning Outcomes |
Learning and teaching strategies |
Assessment |
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After the completion of the course the students will be able to: CLO146- Students will get ideas about the individual-based models of infectious diseases. These models allow us to incorporate stochastic effects, and individual-scale detail in ways that cannot be captured in more traditional models. CLO147- Students review a framework based on directed random networks that unifies a range of individual-based models in closed populations, simplifying their analysis. We then show how this framework provides a new and potentially useful perspective on the design of vaccination strategies. Student will also get idea about reproduction number which is used to control epidemics. CLO148- Students get ideas about The types of simulations, simulation languages, pseudo-random numbers, Marcov chain and variants from different probability distributions. CLO149- Students learn about the systems and its type, mathematical modeling , simulation there advantages and drawbacks. CLO150- Students learn how to do modelling through graph, LPP.
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Approach in teaching: Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching Learning activities for the students: Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical
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Presentations by Individual Students Class Tests at Periodic Intervals. Written assignment(s) Semester End Examination |
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).
- D. N. P. Murthy, N. W. Page, E. Y. Rodin, Mathematical Modeling, Pergamum Press,2013.
- J. N. Kapoor, Mathematical Modeling, Wiley Eastern Ltd.,2015
- P. Fishwick,Simulation Model Design and Execution, PHI, 1995
- Brian Albright, Mathematical Modeling with Excel, Jones & Bartlett,2012.
- A. M. Law, W. D. Kelton,Simulation Modeling and Analysis, McGraw-Hill, 2007.
- J. A. Payne, Introduction to Simulation, Programming Techniques and Methods of Analysis, Tata McGraw Hill Publishing Co. Ltd., 1988.
- V.P. Singh, System Modeling & Simulation, New Age International Publishers, 2009.
