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.

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.