Mathematical modeling of adaptive immune response after transplantation

2020 ◽  
Vol 13 (08) ◽  
pp. 2050167
Author(s):  
Anka Markovska
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Immune Response ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Cellular Immunity ◽  
Adaptive Immune Response ◽  
Nonlinear Ordinary Differential Equations ◽  
Adaptive Immune

A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.

scholarly journals Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy

2016 ◽  
Author(s):  
Kathleen P. Wilkie ◽  
Philip Hahnfeldt ◽  
Lynn Hlatky
Keyword(s):  
Mathematical Modeling ◽  
Immune Response ◽  
Differential Equations ◽  
Tumor Growth ◽  
Ordinary Differential Equations ◽  
Systemic Disease ◽  
Growth Dynamics ◽  
Tumor Dormancy ◽  
Cytotoxic Action ◽  
General Method

AbstractCancer is not solely a disease of the genome, but is a systemic disease that affects the host on many functional levels, including, and perhaps most notably, the function of the immune response, resulting in both tumor-promoting inflammation and tumor-inhibiting cytotoxic action. The dichotomous actions of the immune response induce significant variations in tumor growth dynamics that mathematical modeling can help to understand. Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.

scholarly journals Role of the cellular immunity in the formation of the immune response in coronavirus infections

2021 ◽  
Vol 23 (6) ◽  
pp. 1229-1238
Author(s):  
I. A. Ivanova ◽  
N. D. Omelchenko ◽  
A. V. Filippenko ◽  
A. A. Trufanova ◽  
A. K. Noskov
Keyword(s):  
Immune Response ◽  
T Cells ◽  
Cellular Immunity ◽  
Memory T Cells ◽  
Adaptive Immune Response ◽  
Cell Immune Response ◽  
Adaptive Immune ◽  
Specific Memory ◽  
Causative Agents

The data obtained during previous epidemics caused by coronaviruses, and current pandemic indicate that assessing the role of certain immune interactions between these viruses and the microorganism is the main pre-requisite for development of diagnostic test systems as well as effective medical drugs and preventive measures. The review summarizes the results of studying patho– and immunogenesis of SARSCoV, MERS-CoV, and SARS-CoV-2 infections. These coronaviruses were proven to suppress development of adaptive immune response at the stage of its induction, affecting the number and functional activity of lymphocytes, effectors of cellular immunity, causing impairment of lymphopoiesis, apoptosis and «depletion» of these cells, thus leading to longer duration of the disease and increased viral load. Information about the role of cellular immunity in development of immune response to coronaviruses is presented. It was proven that the causative agents of SARS, MERS and COVID-19 trigger adaptive immune response in the microorganism according to both humoral and cellular types. Moreover, the synthesis of specific immunoglobulins does not yet point to presence of protective immune response. Activation of the cellular link of immunity is also important. A high degree of antigenic epitope homology in SARS-CoV, MERS-CoV and SARS-CoV-2 is described, thus suggesting an opportunity for cross-immunity to coronaviruses. The review addresses issues related to the terms of specific memory immune cells to SARS-CoV, MERS-CoV and SARS-CoV-2, and their role in providing long-term protection against these infections. Given that specific antibodies to SARS and MERS pathogens persisted for a year, were often not detected or briefly registered in patients with mild and asymptomatic infections, we can talk about important role of the cellular immune response in providing immunity to these coronaviruses. It was shown that, in contrast to antibodies, the antigen-specific memory T cells were registered in patients with SARS virus for 4 to 11 years, and Middle East Respiratory Syndrome – up to two years. Further research is needed to determine presence and number of memory T cells in COVID-19. A comparative analysis of data obtained during previous epidemics with respect to formation of adaptive immunity to coronaviruses. Description of proteins and epitopes recognized by human T lymphocytes will be useful in monitoring immune responses in COVID-19 patients, as well as in developing informative tests to study T cell immune response to SARS-CoV-2 and new preventive drugs.

scholarly journals Mathematical Modelling of Immune Response in Tissues

2009 ◽  
Vol 10 (1) ◽  
pp. 9-38 ◽  
Author(s):  
B. Su ◽  
W. Zhou ◽  
K. S. Dorman ◽  
D. E. Jones
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Chronic Infection ◽  
Adaptive Immune Response ◽  
Cell Movement ◽  
Antigen Recognition ◽  
Innate Immune ◽  
Adaptive Immune ◽  
Pde Model ◽  
Persistent Antigen

We have developed a spatial–temporal mathematical model (PDE) to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition). The PDE model is robust to variation in antigen load and it can account for (1) antigen recognition, (2) an innate immune response, (3) an adaptive immune response, (4) the elimination of antigen and subsequent resolution of the immune response or (5) equilibrium of the immune response to the presence of persistent antigen (chronic infection) and the formation of a granuloma.

scholarly journals A mathematical model of p62-ubiquitin aggregates in autophagy

2021 ◽  
Vol 84 (1-2) ◽  
Author(s):  
Julia Delacour ◽  
Marie Doumic ◽  
Sascha Martens ◽  
Christian Schmeiser ◽  
Gabriele Zaffagnini
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Asymptotic Methods ◽  
Finite Size ◽  
Rigorous Results ◽  
The Third ◽  
Cellular Autophagy ◽  
Free Particles

AbstractAggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.

scholarly journals Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Jaouad Danane ◽  
Karam Allali
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Steady State ◽  
Adaptive Immunity ◽  
Reproduction Number ◽  
Adaptive Immune Response ◽  
Hiv Model ◽  
Adaptive Immune ◽  
The Impact ◽  
Ctl Immune Response

In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number R0, the CTL immune response reproduction number R1z, the antibody immune response reproduction number R1w, the antibody immune competition reproduction number R2w, and the CTL immune response competition reproduction number R3z. On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for R0 is performed in order to check the impact of different input parameters.

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