Modeling the Dynamics of Bacteremic Pneumonia: The role of Control Strategies, Case Detection and Treatment

Abstract

Pneumonia is a respiratory disease mainly caused by bacteria, Streptococcus Pneumoniae. The bacteria exist in up to 90 different strains out of which 25 are invasive. Pneumonia is one of the leading causes of mortality in the developing countries claiming about 1.9 million lives per year. Deaths due to pneumonia can occur within 3 days of illness and any delay of treatment may not save live. Hence prompt and effective control measures for the disease is needed. Integrating mathematical modeling in epidemiological research is important in studying dynamics and identifying effective control measures. In this study therefore, we developed mathematical models to study the dynamics of pneumonia and assessed the optimal control strategy in a community. The models were analyzed by applying the theory of ordinary differential equations and dynamical systems to determine if there is a point where equilibrium appears, disappears, change stability or conditions necessary for the disease to invade. Finally, a Monte Carlo Markov Chain (MCMC) simulation technique was used to simulate data for transmission parameters when vaccination and treatment are used as control strategies. A kernel density estimation was then used to estimate probability distribution of the transmission parameters. The results show that eliminating carriers in a population is an important strategy in reducing the disease burden since it reduces the value of basic reproduction number, Ro. The use of both vaccination and treatment control strategies showed a significant reduction on disease dynamics; however using treatment alone is not significant. Using case detection strategy is important in reducing the disease incidence. A detailed analysis of the simulated transmission data leads to probability distribution of R; as opposed to a single value in the conventional deterministic modeling approach hence a better estimation for transmission parameter realized. We recommend that at least 22% of the serotype be covered in any vaccine to be used in at least 54% of the population to guarantee efficiency of such vaccination strategies. We also recommend a case detection strategy whenever possible in a population.