INTRODUCTION:
Mathematical modeling is a discipline, which deals with the study of infectious diseases in a population. It is concerned with all aspects of epidemic, e.g. spread, control, vaccination strategy etc. The aim of epidemic modeling is to understand and if possible control the spread of the disease. Immunology is a branch of biomedical science which deals with an organism’s response towards an invading environmental factor.bio species have dedicated cells or tissues to deal with the threat of infection. Some of these responses happen immediately so that an infecting agent can be quickly contained. Other responses are slower but are more tailored to the infecting agent. Collectively, these protections are known as the immune system.
The human immune system is essential for our survival in a world full of potentially dangerous microbes, and serious impairment of even one arm of this system can predispose to severe, even life-threatening, infections.
The immune system is a network of cells, tissues, and organs that work together to defend the body against attacks by “foreign” invaders. These are primarily microbes—tiny organisms such as bacteria, parasites, and fungi that can cause infections. Antibodies are proteins made by the immune system to fight antigens, such as bacteria, viruses, and toxins.
Immunoglobulin M (IgM), which is found mainly in the blood and lymph fluid, is the first antibody to be made by the body to fight a new infection.
Infection occurs when a pathogen invades body cells and reproduces. Infection will usually lead to an immune response. If the response is quick and effective, the infection will be eliminated or contained so quickly that the disease will not occur.
Sometimes infection leads to disease. Disease can occur when immunity is low or impaired, when virulence of the pathogen is high, and when the number of pathogens in the body is great.
NUMERICAL SOLUTION:
In this paper I am trying to investigate the mathematical relation between immunity system and antigens. I am defining two variables such that those two variables can represent the percentage of total population of cells that are susceptible and infected cells in an individual.
Let s be the population of susceptible in an individual and I be the infected population of individuals.
C= S+I
Change in susceptible is due to increase in infection. Assume that increase in infection causes reduce in the population of susceptible.
S1 α
Hence S1 =
(1)
Where k is proportionality constant.
So the solution of the above differential equation is
,
where c is constant.
So 
(2)
Where 
is constant.
From equation (2) , if I > S then there is an influence on immunity system.
If I < S then immunity system functions are going absolutely fine.
CONCLUSION:
In this paper my intention is to prove in an individual an immunity system was playing important role in spreading diseases. The immune system protects the body like a guardian from harmful influences from the environment and is essential for survival. Although I observed every bio species have its own immunity system, I accepting its own priority in entire system.
ACKNOWLEDGEMENT:
Our sincere thanks to our beloved madam Dr. Smt. P. ChiranjeeviniKumari, M.A., Ph.D.,
Secretary and Correspondent, Director of P.G.Courses,Ideal College of Arts and Sciences, Kakinada
REFERENCES:
1. “Differential equations and their applications” by zafarahsan.
2. “Differential equations, dynamical systems, and as introduction chaos” by Morris W.Hirsch,Stephen Smale, Robert L. Devaney
3. SIR model by David Smith and Lang Moore.
4. Images from Google search engine and Wikipedia.