"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Biomathematics
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
ME278
2
2+1+1
7
compulsory
Matematică Aplicată
Teaching Staff in Charge
Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro
Aims
Main models from biology are presented.
Content

1. Population dynamics: single species models; Lotka-Volterra type
models; equilibrium solutions; stability; hysteresis.
2. Reaction-diffusion systems: conservation equation;
reaction-diffusion mechanisms; Turing's theory on diffussion-driven
instability; spatial pattern with reaction-diffusion mechanisms;
applications in morphogenesis.
3. Mathematical models in epidemiology: SIR models; methods of
nonlinear analysis for the treatment of nonlinear equations from
biomathematics; geographic spread of epidemics; travelling wave
solutions.

References
1. J.D. Murray, Mathematical Biology, Springer, Berlin, 1989.
2. F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, Berlin, 2001.
3. R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.
4. R. Precup, Ecuatii cu derivate partiale, Transilvania Press, Cluj, 1997.
Assessment
written examination