Epidemic dynamical models

- Description of a given real problem, determination of all variables and parameters, which will be investigated.

- Determination of basic assumptions about the given problem. Computation of mathematical formulas by means of the assumptions.

- Construction of a mathematical model in the form of one or more differential equations.

- A brief overview of definitions and theorems from the theory of ordinary differential equations and dynamical systems, needed to investigation of the model.

- Determination of critical points and phase portraits.

- Investigation of a dependence of the phase portraits on changes of parameters contained in the model.

- Creation of phase portraits for given values of parameters by a mathematical software.

Literature:

F. Brauer, C. Castillo-Chávez: Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.

J. Hale, H. Kocak: Dynamics nad Bifurcations. Springer, New York 1991.

D.W. Jordan, P.Smith: Nonlinear Ordinary Dierential Equations, Oxford Univ. Press, 1999.

L. Perko: Dierential Equations and Dynamical Systems. Springer, New York 1991.

J. Kalas, M. Ráb: Obyčejné diferenciální rovnice. Brno 1995.