Modeling animal responses to environmental changes and pressures

Daozhou Gao

Cleveland State University (Mathematics)

"Influence of Changes in Population Movement on Total Biomass"

How animal dispersal affects the total population abundance and its distribution in a heterogeneous environment is a fundamental question in spatial ecology. In this talk, based on a multi-patch logistic model with asymmetrical migration, we study the dependence of the global and local biomass on the dispersal intensity and dispersal asymmetry. In particular, the total biomass over two patches is either constant, or strictly decreasing, or strictly increasing, or initially strictly increasing then strictly decreasing with respect to dispersal rate. On the other hand, we develop a novel population model with both migration and visitation and show that the presence of visitation can substantially change the influence of population migration on population abundance. This is a joint work with Yuan Lou and Yutong Zhang.
Additional authors: Yuan Lou (Shanghai Jiao Tong University); Yutong Zhang (Shanghai Normal University).

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Xi Huo

University of Miami (Mathematics)

"Linking mosquito trap data with models: identifiability, fitting, and applications"

Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this talk, I will show how we incorporate local entomological and temperature data in an ODE model, investigate the parameter identifiability, and fit the model to mosquito trap data from 2017 to 2019. The well-calibrated model can help us compare the Ae. aegypti population, evaluate the impact of rainfall intensity in different urban built environments, and assess the effectiveness of vector control strategies in Miami-Dade County.
Additional authors: Jing Chen; André B.B. Wilke; John C. Beier; Chalmers Vasquez; William Petrie; Robert Stephen Cantrell; Chris Cosner; Shigui Ruan

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Marco Tosato

Western University (Applied Mathematics)

"Impact of deer migration on tick population dynamics"

Ticks are the carriers of several vector-borne diseases worldwide. In the past few decades, they have been spreading northward across Canada and have reached areas that were originally tick-free. In this talk, we explain how the interaction between deer mobility and tick population might have played a relevant role in this. In particular, we show using a coupled system of ordinary and delay differential equations in a two-patch environment how deer migration affects tick population dynamics and may modify their suitability for specific patches.
Additional authors: Dr. Xingfu Zou

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Tianyu Cheng

Western University, Canada (Department of Mathematics)

"Modelling the impact of society precaution on disease dynamics and its evolution"

Afraid of infection, uninfected individuals may spontaneously protect themselves against infectors in varying degrees, depending on the severity of epidemics. As a result of adopting non-pharmaceutical inventions, people almost exhibit a uniform protection level without individual differences. We introduce a mathematical model formulated by differential equations to describe the severity of epidemics and group-precaution levels relying on the severity level during the epidemics. Our model describes that the group-precaution level mainly affects the severity of epidemics by directly adjusting the number of practically susceptible; In turn, the severity change of epidemics leads to the evolution of the group-precaution level. Mathematical analysis shows that when basic reproduction number is larger than 1, the endemic equilibrium exists and is subjective to a critical parameter that combines the initial protection level and the initial number of the infectious class. Considering the time lag in responding to the severity change of epidemics, we further extend our model, which is a system of delay differential equations. We figure out the condition that Hopf bifurcations occur by theoretical and numerical techniques.

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