A Model for Childhood Pneumonia Dynamics (original) (raw)

2014, Journal of Life Sciences Research

This work is licensed under a Creative Commons Attribution 3.0 License Asian Online Journal Publishing Group 1. Introduction Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites which is characterized primarily by inflammation of the alveoli in the lungs or by alveoli that are filled with fluid. Bacteria and viruses are the primary causes of pneumonia. When a person breath pneumonia-causing pathogens into his lungs and the body's immune system cannot prevent entry, the organisms settle in the small air sacs called alveoli and continue to multiply. The host body sends white blood cells to attack the infection causing the sacs to be filed with fluid and pus-causing pneumonia. The people most susceptible to Pneumonia are the old, infants, the sick and those with impaired immune systems [1]. According to WHO, childhood pneumonia can be spread through inhaling viruses and bacteria, airborne droplets from a cough or sneeze, direct contact or through blood, especially during and shortly after birth. Pneumonia symptoms include cough, custy or green mucus coughed up from lungs, fever, fast breathing and shortness of breath, chills, chest pain that usually worsens when taking a deep breath , fast heartbeat, fatigue and feeling very weak, nausea and vomiting, diarrhea, sweating, headache, muscle pain, confusion or delirium and dusky or purplish skin color (cyanosis) from poorly oxygenated blood [2-4]. Childhood pneumonia is a major public health issue for Kenya. In 2008, joint report by Unicef and WHO pneumonia was described as 'forgotten killer of children' because it was the second cause of death among less than fives years, claiming equivalent to 16 % of child mortality in Kenya. According to WHO, Pneumonia can be This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of therapy. The model is based on the Susceptible-Infected-Treatment-Susceptible compartmental structure with the possibility of infected individual recovering from natural immunity. Important epidemiological thresholds such as the basic and control reproduction numbers (and respectively) and a measure of treatment impact are derived. Infection free point was found to be locally stable but globally unstable. We found that if the control reproduction number is greater than unity, then there is a unique endemic equilibrium point and it is less than unity, the endemic equilibrium point is globally asymptotically stable, and pneumonia will be eliminated. Numerical simulations using Matlab software suggest that, besides the parameters that determine the basic reproduction number, natural immunity plays an important role in pneumonia transmissions and magnitude of the public health impact of therapy. Further, treatment regimens with better efficacy holds great promise for lowering the public health burden of pneumonia disease.