Title : Differential equation modelling and analysis
Abstract:
The presentation consists of Mathematical modelling and Mathematical Epidemiology. The real life problems can be stated as Mathematical models and analysed. Here, we mainly discuss the mathematical models on Infectious diseases. It states the basic SIR models in Differential Equations and the concepts of parameters, state variables, and control variables. We discuss the types of Differential equations such as Ordinary differential equations (ODE), Partial Differential Equations (PDE), Delay differential Equations (DDE), Fractional differential equations (FDE).
It explains the methodologies such as Boundedness, Positiveness, Existence and Uniqueness of solutions, Equilibrium Points, Local stability by RH Criteria, Global Stability by Lyapunov Theorem, Basic reproduction method by next generation matrix method, Optimal controls by Pontryagin s Maximum Principle, Sensitivity Analysis, Bifurcation Analysis and Numerical Analysis in Disease modelling.
