https://link.springer.com/content/pdf/10.1007%2Fs11538-016-0214-9.pdf

Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

Thermostatted kinetic equations as models for complex systems in physics and life sciences.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

This paper is concerned with the mathematical modeling of complex systems characterized by particles refuge. Specifically the paper focuses on the derivation and moments analysis of thermostatted kinetic frameworks with conservative and nonconservative interactions for closed and open complex systems at nonequilibrium. Applications and future research perspectives are discussed in the last section of the paper.

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Modeling Complex Systems with Particles Refuge by Thermostatted Kinetic Theory Methods

In this paper we study a mathematical model formulated within the framework of the kinetic theory for active particles The model is a bilinear system of integro-differential equations IDE of Boltzmann type and it describes the interactions between virus population and the adaptive immune system The population of cytotoxic T lymphocytes is additionally divided into precursor and effector cells Conditions for existence and uniqueness of the solution are studied Numerical simulations of the model are presented and discussed

On a Mathematical Model of Adaptive Immune Response to Viral Infection

In this paper we present a mathematical model formulated within the framework of the kinetic theory for active particles. The model is a bilinear system of integro-differential equations of Boltzmann type and it describes the interactions between virus population and the adaptive immune system. The population of cytotoxic T lymphocytes is additionally divided into precursor and effector cells. The effects of the parameters describing the proliferation and differentiation of cytotoxic T lymphocytes are studied numerically.

Adaptive immunity and CTL differentiation - a kinetic modeling approach

In this paper we present a new mathematical model describing acquired immune response to viral infection. The model is formulated as a system of six ordinary differential equations (ODE). Conditions for existence, uniqueness and non-negativity of the solutions are studied. Numerical simulations for the case of dominating cellular immunity and various initial values of concentrations of virus particles are presented and discussed.

Ana Markovska

Papers

Adaptive immunity and CTL differentiation - a kinetic modeling approach

On a Mathematical Model of Adaptive Immune Response to Viral Infection

Numerical Investigation of Adaptive Immune Response to Viral Infection