modelling childhood pneumonia and its implications regarding its control using kenyan data

Abstract

Pneumonia is an infection of the lungs. It is caused by bacteria, viruses, fungi or parasites, among others. Despite childhood pneumonia of the under five years of age still accounting for about 16% death in Kenya, there was no reliable deterministic mathematical model which had incorporated data and/or parameters from UNICEF and Kenya Health Information System (KHIS) to qualitatively and/or quantitatively give more insights to the pneumonia dynamics. This study developed a deterministic model describing population dynamics of the pneumonia of under five years of age in Kenya and suggested possibly the best control strategies. The objectives were to: develop a model of pneumonia for the under the age five with Kenya specific attributes, determine model thresholds as well as perform analysis of stability, backward bifurcation and sensitivity so as to establish the conditions for the spread of disease, estimate numerical results of model using data and/or parameters from KHIS and UNICEF as well as evaluate normalized sensitivity index and perform numerical simulations to validate analytical results of the model and finally assess the effects of efficacy of the vaccination, environmental factors and therapeutic treatment drugs. Susceptible-Infected-Recovered- Susceptible (SIRS) infectious disease classical model was modified to develop a population based model flow chart. The study considered the status of pneumonia infection, status of vaccination and essential features of pneumonia when formulating the flow chart. Expression was determined from the eigenvalues of the next generation matrix. Sensitivity analyses of various parameters were carried out using partial differentiation. Kenya secondary data and parameters from KHIS and UNICEF of the under five years of age for the years 2012 and 2013 were used in the developed model and also the prediction of the dynamics estimated model for a period of twenty years was determined using 2013 as the initial year. The first order nonlinear differential equations which described pneumonia dynamics were deduced from the flow chart. The algebraic expression of was obtained as the spectral radius of next generation matrix and its estimated numerical value was obtained as 9.31808.The estimated model was obtained through using data and parameters from UNICEF and KHIS. The numerical sensitivity analysis of various parameters was carried out analytically and their estimated numerical results were shown graphically. The Kenya population data from UNICEF and KHIS was used to carry out numerical simulations of the estimated model with 2013 as initial condition. Numerical simulation was carried out for a period of twenty years in Kenya and results obtained graphically. The results of simulations showed that the number of outpatients and inpatients in twenty years’ time were expected to vary from 353000 and 4279 in 2013 to about 240000 and 1000 in 2033 respectively. The obtained numerical value for was very high because one infected child is likely to infect 9.31808 other susceptible children in presence of current interventions. The Government of Kenya should strive to attain critical treatment rates whose expressions are provided as it is not possible to attain 100% treatment rates. The sensitivity analysis showed that addressing overcrowding which increases contact rates and improving vaccination drug’s efficacy among other factors would lower pneumonia burden. Further research should consider the effect of hospital acquired pneumonia as this study only considered community acquired pneumonia.