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Open AccessMathematical modelling of vaccination rollout and NPIs lifting on COVID-19 transmission with VOC: a case study in Toronto, Canada
Since December 2020, public health agencies have implemented a variety of vaccination strategies to curb the spread of SARS-CoV-2, along with pre-existing Nonpharmaceutical Interventions (NPIs). Initial strate...
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Chapter
Evaluating the Risk of Reopening the Border: A Case Study of Ontario (Canada) to New York (USA) Using Mathematical Modeling
Many countries have adopted border closures and other jurisdictions (provinces, states, cities, etc.) to control the spread of SARS-CoV-2. Such measures have significantly restricted population movement and ha...
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Reference Work Entry In depth
Time-Delayed Neural Networks: Stability and Oscillations
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Article
On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis
We present an age-structured model for erythropoiesis in which the mortality of mature cells is described empirically by a physiologically realistic probability distribution of survival times. Under some assum...
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Article
Transit and lifespan in neutrophil production: implications for drug intervention
A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino’s extension to the Fr...
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Living Reference Work Entry In depth
Time-Delayed Neural Networks: Stability and Oscillations
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Article
Normal and pathological dynamics of platelets in humans
We develop a mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this informati...
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Chapter
Outgrowing Neurological Diseases: Microcircuits, Conduction Delay and Childhood Absence Epilepsy
The study of familial disorders characterized by recurring changes in neurodynamics, such as epileptic seizures, paralysis and headaches, provide opportunities to identify the mechanisms for dynamic changes in...
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Book and Conference Proceedings
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Reference Work Entry In depth
Time-Delayed Neural Networks: Stability and Oscillations
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Article
Threshold dynamics in an SEIRS model with latency and temporary immunity
A disease transmission model of SEIRS type with distributed delays in latent and temporary immune periods is discussed. With general/particular probability distributions in both of these periods, we address th...
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Chapter
Introduction to Dynamics in Nonlinear Difference and Differential Equations
Nonlinear dynamics is a branch of mathematics that deals with rhythms in nonlinear equations. There is an emphasis on qualitative aspects of dynamics. For example, does a particular set of equations display a ...
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Chapter
Cell Replication and Control
Though all blood cells are derived from hematopoietic stem cells, the regulation of this production system is only partially understood. Negative feedback control mediated by erythropoietin and thrombopoietin ...
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Article
Spatial effects in modeling pharmacokinetics of rapid action drugs
We develop a model to describe the time course of plasma concentration of neuromuscular blocking agents used as anesthetics during surgery. This model, which overcomes the limitations of the classical compartm...
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Article
Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two param...
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Article
Stability in a model of a delayed neural network
The stability of the null solution in a system of coupled cells is investigated. Each cell evolves according to Hopfield's equation for an analog circuit, with a delay incorporated to account for finite switch...
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Article
Feedback and delays in neurological diseases: A modeling study using gynamical systems
Numerous regulatory mechanisms in motor control involve the presence of time delays in the controlled behavior of the system. Experimentally, we have shown that an increase of the time delay in visual feedback...
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Book reviews
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Book
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Chapter
Lifespans in Population Models: Using Time Delays
Population models with a compartment structure have to incorporate the duration of stay in each class. Using a two-compartment model of the regulation of blood cell production, we investigate two elimination m...
