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This paper proposes an alternative approach to modelling relapse in cancer. In particular, the dynamic model for the tumor or biomarker will be subjected to a lower elastic boundary at which the process either will be absorbed or reflected. The likelihood of reflection then can be interpreted as...
An extension of a previously proposed theory for the pathogenesis of AIDS is presented and analyzed using a mathematical modelling approach. This theory is based on the observation that human immunodeficiency virus type 1 (HIV-1) predominantly infects and replicates in CD4 + -T cells, and that...
Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it...
We address the global stability issue for some discrete population models with delayed-density dependence. Applying a new approach based on the concept of the generalized Yorke conditions, we establish several criteria for the convergence of all solutions to the unique positive steady state. Our...
In this paper, we propose a new receptor-based model for pattern formation and regulation in a fresh-water polyp, namely hydra. The model is defined in the form of a system of reaction–diffusion equations with zero-flux boundary conditions coupled with a system of ordinary differential...
Many animals spend a large proportion of their time either foraging for food or watching out for predators (antipredator vigilance). There have been many theoretical and empirical studies investigating the trade-off between these two activities, especially in birds. Previous models of...
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