| A formal species notion based on identical ancestor points Samuel Alexander US Securities and Exchange Commission |
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UT-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
| A modified May Holling Tanner Model: the role of dynamic alternative resources on species' survival Anuraj Singh Engineering Sciences, IITM Gwalior |
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UT-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
| The Problem of Viability in Mathematical Epidemiology Peter Rashkov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences |
We address the problem of viability, or existence of solutions of the controlled dynamical system that share a given set of properties, namely solutions that respect a given upper bound on the phase variable (in our case the size of the infected human compartment) subject to the control function taking values in a given compact set. Such transient dynamic behaviour of the solutions can be studied using viability kernels, which represent the largest set of initial states of the dynamical system such that the proportion of infected individuals is sustained below a given ceiling for all future times. Our goal is to characterise the viability kernel, and we focus on a level-set approach based on Bellman's value function satisfying a dynamic programming principle. This approach allows kernels with positive Lebesgue measure to be approximated numerically even for systems of higher dimensions.
As examples we study several models for vector-borne diseases of Susceptible-Infected or Susceptible-Infected-Recovered type for the human host, and Susceptible-Infected for the mosquito vector, as well as a two-patch system with human mobility based on the Lagrangian modelling framework. The epidemic control is based on the use of mosquito repellents in clothing and the control function takes values constrained by the maximum proportion of the host population employing the repellent-treated clothes. The inspiration for this work originates from COST Action 16227 Investigation and mathematical analysis of the effects of avantgarde disease control via mosquito nano-tech-repellents (2017-2022), funded by EU Horizon 2020 Framework Programme.
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UT-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
| Exploring Toxicity and Model Bias in Adaptive Cancer Therapy Kathleen Wilkie Department of Mathematics, Toronto Metropolitan University |
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UTC-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
| Approaches to modeling bird migration and the transmission dynamics of bird flu among migration birds Ringsong Liu Department of Mathematics and Statistics, University of Wyoming |
Second, another approach to modeling bird migration is proposed, in which there is a region where birds do not move but spend time breeding. Birds leave this breeding region and enter a migration flyway which is effectively a one-way corridor starting and ending at the breeding location. Mathematically, the flyway is a curve parametrized by arc-length. Flight speed depends on position along the flyway, to take account of factors such as wind and the pausing of birds at various locations for wintering or stopovers. Per-capita mortality along the flyway is both position and age-dependent, allowing for increased risks at stopover locations due to predation, and increased risks to immature birds. We also model indirect transmission, via contact with viruses, of avian influenza in migratory and nonmigratory birds, taking into account age structure. Sufficient conditions are obtained for the local stability of the disease-free equilibrium (for a species without migration) and for the disease-free periodic solution (for a migratory species). The birds have specific sites for breeding and winter feeding, and usually several stopover sites along the migration route, and therefore a patch model is the natural choice. However, we also model the journeys of the birds along the flyways, and this is achieved using a continuous space model of reaction-advection type. In this way proper account is taken of flight times and in-flight mortalities which may vary from sector to sector, and this information is featured in the ordinary differential equations for the populations on the patches through the values of the time delays and the model coefficients. The seasonality of the phenomenon is accommodated by having periodic migration and birth rates.
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UTC-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472