Abstract
Center manifold and normal form theories as well as numerical simulations are employed to analyse the bifurcation and stability of a 13-dimensional deterministic model associated with the transmission dynamics of two diseases within a host population. The stability of the multiple equilibrium solutions together with the associated possible critical points are discussed. It is shown that model can only undergo static bifurcations. Owing to the fact that the system exhibits a double-zero singularity, center manifold and normal form theories are used to reduce the model to a two-dimensional system. A detailed bifurcation and stability analysis is given for the behaviour of the system in the vicinity of the critical point. A robust finite-difference method is developed and used for the solution of the 13-D system. Unlike some conventional numerical schemes, this novel scheme does not suffer from scheme-dependent instabilities. The numerical method gives results that are consistent with the theoretical predictions.
Original language | English (US) |
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Pages (from-to) | 317-330 |
Number of pages | 14 |
Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms |
Volume | 10 |
Issue number | 1-3 |
State | Published - Feb 2003 |
Externally published | Yes |
Keywords
- Bifurcation and stability
- Center manifold
- Equilibrium solution
- Finite-difference method
- Normal form
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics