# Mathematical Model For The Spread And Control Of Tuberculosis Disease

Mathematical Model For The Spread And Control Of Tuberculosis Disease

## Chapter One

### 1.0 Introduction

#### 1.1 Background of the Study

Tuberculosis or TB (short for Tubercles Bacillus) is an air borne and highly infectious disease caused by infection with the bacteria mycobacterium tuberculosis. An individual is infected with the disease when he or she inhales the TB germs which are released into the air when infected individuals cough, sneeze, spit or talk.

The first period of infection is the period of Latency when individual exhibits no symptoms of the disease and is not infectious to others. Such an individual is said to have Latent TB infection. ( A.U. Kalu and S.C. Inyama 2012), The Latent period can be extremely variable as a great majority ( 90 %) may live with the disease as long as possible without it progressing to Active TB whereas a small proportion ( 10 %) will progress to Active TB infection, falling ill within months or several years after infection.

The second stage is the period of Active TB infection when the individual start to exhibit some or all the symptoms of TB.

The highest risk group to acquire TB when exposed to it are children under five years of age, persons who are immuno compromised (i.e. have weakened immunity), especially those who are HIV-Positive, persons who have diabetes or kidney failure, people that take excessive alcohol and drugs, those with poor nutrition and lack of food, those suffering from stress and those living in poorly ventilated rooms.

Tuberculosis usually attacks the lungs but can also attack other parts of the body like the kidney, Spine, brain, bones, joints etc. The classic symptoms of TB of the lungs are a chronic cough which may result in blood-tinged sputum, fever, loss of appetite, weight loss and fatigue, Infection of other organs causes a wide range of symptoms. Pneumonia, lung collapse and enlarged lymph nodes may also occur.

Two forms of tuberculosis that become life- threatening are:

1. Miliary TB, which means the bacteria have spread throughout the lungs and into the bloodstream.
2. TB meningitis (infection of the covering of the spinal cord and /or brain by TB bacteria).

Diagnosis relies on radiology (commonly chest X- ray), a tuberculin skin test, blood tests, as well as microscopic examination and microbiological culture of bodily fluids (such as sputum).

The infectiousness of a TB patient is directly related to the number of droplet nuclei carrying M. tuberculosis (tubercle bacilli) that are expelled into the air. Depending on the environment, these tiny particles can remain suspended in the air for several hours. M. tuberculosis is transmitted through the air, not by surface contact. Infection usually occur when a person inhales droplet nuclei containing M. tuberculosis, and the droplet nuclei traverse the mouth or nasal passages, upper respiratory tract, and bronchi to reach the alveoli of the lungs.

Environmental factors that enhance the probability that m. tuberculosis will be transmitted are:

Concentration of infectious bacilli suggest that the more baccili in the air, the more probable that M.tuberculosis will be transmitted.

Space; This is an exposure in small, enclosed space.

Ventilation is inadequate local or general ventilation that results in insufficient dilution or removal of infectious droplet nuclei.

Air circulation is the recirculation of air containing infectious droplet nuclei.

Specimen handling, improper specimen handling procedures generate infectious droplet nuclei.

Air pressure ; this is a positive air pressure in infectious patientโs room that causes M.tuberculosis organisms to flow to other areas.

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