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Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response

F. Gazori, M. Hesaaraki (2015)

Applicationes Mathematicae

In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence...

Modeling the role of constant and time varying recycling delay on an ecological food chain

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2010)

Applications of Mathematics

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...

Modelling Tuberculosis and Hepatitis B Co-infections

S. Bowong, J. Kurths (2010)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...

Models of interactions between heterotrophic and autotrophic organisms

Urszula Foryś, Zuzanna Szymańska (2009)

Applicationes Mathematicae

We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.

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