Applications of homogeneous maps to mathematical models arising from epidemiology and ecology

February 7, 2025

TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Dr. Feng-Bin Wang (fbwang0229@gmail.com), (fbwang@mail.cgu.edu.tw) , Division of Natural Science, Center for General Education, Chang Gung University, Taiwan.

ABSTRACT:

In this talk, we first introduce a mathematical model describing the mosquito growth incorporating metamorphic stages (including aquatic stage and adult stage), mating behavior and the spatial movement of adult mosquitoes in a seasonal environment. Our model is a reaction-diffusion system governing the dynamics of the aquatic mosquitoes, the matured male mosquitoes, and matured female mosquitoes. The threshold dynamics of the governing system in a bounded habitat can be determined by the basic reproduction ratio of mosquitoes, which is defined by  a time-periodic homogeneous evolution system without compactness. The propagation phenomena, including the existence of the spreading speeds and almost pulsating waves will be also mentioned. For the second part of this talk,  we shall introduce variable-internal-stores models in a flowing habitat/chemostat with temporal-spatial variations, where two essential nutrients are stored internally within individuals, and  population growth is a positive function of stored nutrients. The threshold type result on the extinction/persistence of the species can be determined by the basic reproduction ratio. The main difficulty in mathematical analysis is caused by the singularity at the extinction state.

HOST: Naveen Vaidya

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