• Publications
  • Influence
Delay Differential Equations: With Applications in Population Dynamics
Delay Differential Equations: Introduction. Basic Theory of Delay Differential Equations. Characteristic Equations. Applications in Population Dynamics: Global Stability for Single Species Models.Expand
Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters
The main objective of this paper is to provide practical guidelines that combine graphical information with analytical work to effectively study the local stability of some models involving delay dependent parameters. Expand
Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays.
Using the mass conservation law, this work introduces two explicit time delays and proposes a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. Expand
Stoichiometry in producer-grazer systems: Linking energy flow with element cycling
A two-dimensional Lotka-Volterra type model is constructed that incorporates chemical heterogeneity of the first two trophic levels of a food chain and expresses producer—grazer interactions in stoichiometrically realistic terms reveals qualitatively new dynamical behavior. Expand
To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic
A compartmental model for assessing the community-wide impact of mask use by the general, asymptomatic public is developed, suggesting face masks are potentially of high value in curtailing community transmission and the burden of the COVID-19 pandemic. Expand
Global qualitative analysis of a ratio-dependent predator–prey system
Abstract. Ratio-dependent predator–prey models are favored by many animal ecologists recently as more suitable ones for predator–prey interactions where predation involves searching process. However,Expand
Uniqueness of limit cycles in Gause-type models of predator-prey systems
This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized LienardExpand
Wavefronts and global stability in a time-delayed population model with stage structure
We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential modelExpand
Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview
An overview of some of the mathematical models appearing in the literature for use in the glucose-insulin regulatory system in relation to diabetes is given, enhanced with a survey on availableExpand