9867

Model of Immune Response with Time-Dependent Immune Reactivity

The probability of getting a disease is related to the efficiency of the immune system, which can change with the seasons of the year. This Demonstration shows the solution of a model of the immune system that has periodic changes in the immune reactivity due to changes in the environment.
The model consists of three delay ordinary differential equations
,
,
,
with initial history functions and ;
is the immune reactivity (the immune response of the infected individual): , and is the antibody production rate per plasma cell due to the presence of antigens. Here , , and represent antigen, plasma cells, and antibody concentrations; is the antigen reproduction rate; is the probability of an antigen-antibody encounter; is the reciprocal of the plasma cell lifetime; is the number of antibodies necessary to suppress one antigen; and is a constant. Values of these parameters are taken from the reference. Time is , is the time delay necessary for the formation of plasma cells and antibodies, and is the length of the season. Large ratios of antibody to antigen concentrations, , correspond to a strong immune system in which reactions are fast and in which the organism has strong resistance; on the other hand, small values of this ratio imply immunodeficiency.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Reference
[1] M. Bodnar and U. Foryś, "A Model of Immune System with Time-Dependent Immune Reactivity," Nonlinear Analysis, 70(2), 2009 pp. 1049–1058. doi:10.1016/j.na.2008.01.031.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+