Continuous-discrete model of parasite-host system dynamics: Trigger regime at simplest assumptions

• Main Authors: L. V. Nedorezov, Neklyudova
• Format: Article
• Language: English
• Published: International Academy of Ecology and Environmental Sciences 2014-09-01
• Series: Computational Ecology and Software
• Subjects: parasite-host system dynamics; mathematical model
• Online Access: http://www.iaees.org/publications/journals/ces/articles/2014-4(3)/continuous-discrete-model-of-parasite-host-system-dynamics.pdf

In paper continuous-discrete model of parasite-host system dynamics is analyzed. Within the framework of model it is assumed that appearance of individuals of new generations of both populations is realized at fixed time moments tk=hk, t0=0, k=1,2,... , h=const>0; it means that several processes are compressed together: producing of eggs by hosts, attack of eggs by parasites (with respective transformation of host's eggs into parasite's eggs), staying of hosts and parasites in phase "egg", and appearance of new individuals. It is also assumed that death process of individuals has a continuous nature, but developments of both populations are realized independently between fixed time moments. Dynamic regimes of model are analyzed. In particular, it was obtained that with simplest assumptions about birth process in host population and numbers of attacked hosts regime with two non-trivial stable attractors in phase space of system can be realized.