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Mathematical modeling of antigenicity for HIV dynamics

François Dubois, Hervé V.J. Le Meur, Claude Reiss (2010)

MathematicS In Action

This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...

Modeling Adaptive Behavior in Influenza Transmission

W. Wang (2012)

Mathematical Modelling of Natural Phenomena

Contact behavior plays an important role in influenza transmission. In the progression of influenza spread, human population reduces mobility to decrease infection risks. In this paper, a mathematical model is proposed to include adaptive mobility. It is shown that the mobility response does not affect the basic reproduction number that characterizes the invasion threshold, but reduces dramatically infection peaks, or removes the peaks. Numerical...

Modelling tumour-immunity interactions with different stimulation functions

Petar Zhivkov, Jacek Waniewski (2003)

International Journal of Applied Mathematics and Computer Science

Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...

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.

Monotonicity properties of oscillatory solutions of differential equation ( a ( t ) | y ' | p - 1 y ' ) ' + f ( t , y , y ' ) = 0

Miroslav Bartušek, Chrysi G. Kokologiannaki (2013)

Archivum Mathematicum

We obtain monotonicity results concerning the oscillatory solutions of the differential equation ( a ( t ) | y ' | p - 1 y ' ) ' + f ( t , y , y ' ) = 0 . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.

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