MATHEMATICAL MODEL OF PNEUMONIA DISEASE DYNAMICS WITH DRUG RESISTANCE IN SOUTH NATION

Abstract

In this study we developed and analyzed a deterministic model for pneumonia disease dynamics with drug resistance in south nation. The model divided the total population in to five compartments, namely Susceptible, vaccinated, Infected, drug resistance and recovered. The qualitative behaviors such as the invariant region, positivity of the solution, equilibrium points and their stabilities are analyzed. The model reproduction number , is derived and the stability of equilibrium points is analysed. The results of the analysis shows that there exist a locally stable disease free equilibrium point, when  1 and a unique endemic equilibrium, when  1.Numerical simulations are carried out by depending on data collected from two hospitals of wolita sodo university referral hospital and durame doctor Bogalech matasabiya general hospital and the results indicate that contact rate and waning rate have a great role to expand the disease. However, treatment rate and vaccinated rate have high contribution to eliminate pneumonia disease in the population. Although,the graph of simulation was running by matlab software and the result shows the basic reproduction number is greater than one, then infected population gragh is increased and basic reproduction number is less than one, then infected population gragh is decreased. generally treatment rate, Vaccinated rate and treatment efficacy values have play an important role to control and minimize the transmition rate of pneumonia disease in the community.We recommend a combination should be decrease in contact between infected and susceptible individuals, creating awareness to decrease contact rate and slow down the emergencey of antibiotic resistance bacteria in the community.