infection: The invasion and multiplication of microorganisms such as bacteria, viruses, and parasites that are not normally present within the body. An infection may cause no symptoms and be subclinical, or it may cause symptoms and be clinically apparent. An infection may remain localized, or it may spread through the blood or lymphatic vessels to become systemic (bodywide). Microorganisms that live naturally in the body are not considered infections. For example, bacteria that normally live within the mouth and intestine are not infections.

Bacteria are microscopic living organisms, usually

one-celled, that can be found everywhere. They

can be dangerous, such as when they cause

infection, or beneficial, as in the process of

fermentation (such as in wine) and that of

decomposition.

White blood cells (WBCs), also

called leukocytes or leucocytes, are the cells of

the immune system that are involved in protecting

the body against both infectious disease and foreign

invaders. All white blood cells are produced and

derived from multipotent cells in the bone

marrow known as hematopoietic stem cells.

Leukocytes are found throughout the body,

including the blood and lymphatic system

How many white blood cells are in the human body?

In normal adult bodies there are 4,000 to 10,000 (average 7,000)

white blood cells per microliter of blood. If the number of white

blood cells in your blood increases, it is a sign of an infection

somewhere in the body.

Neutrophils are active in phagocytosing bacteria and are present in large amount in the pus of wounds. These cells are not able to renew their lysosomes (used in digesting microbes) and die after having phagocytosed a few pathogens. Neutrophils are the most common cell type seen in the early stages of acute inflammation. The life span of a circulating human neutrophil is about 5.4 days.

Let B(t) denote the number of bacteria in a wound

and N(t) the number of neuthrophiles. The bacterial

growth factor is a [bacteria/hour] and the killing

factor of the neuthrophiles b [bacteria/hour] and

assume that the entry rate of new neuthrophiles is u(t)

[neuthrophiles/hour].

We Simulated the system in Simulink with a = 3,b = 1.1,g = 1.5, and

with initial conditions B(0) = 100, N(0) = 0 and let u(t) be a step

with magnitude 10. What happens if a becomes large (> 8)?