Fikru Tessema - Department of Mathematics, Faculty of Natural Science, Wollega University, Nekemt, Ethiopia
Boka Bole - Department of Mathematics, Faculty of Natural Science, Wollega University, Nekemt, Ethiopia
Purnachandra Rao - Department of Mathematics, Faculty of Natural Science, Wollega University, Nekemt, Ethiopia

Pneumonia is a very serious infectious disease that affects one or two sides of the human lungs. The disease is caused by infectious agents such as bacteria, viruses and fungi. In general, pneumonia is caused by Streptococcus bacteria. In present paper, we developed and analyzed the optimal control and cost-effectiveness strategies for pneumonia with the inclusion of a drug resistance compartment. The basic reproduction number that governs disease transmission has been obtained as the largest eigenvalue of the next-generation matrix. Both local and global stabilities of the disease-free equilibrium and endemic equilibrium points of the model equations were established using basic reproduction numbers. It is found in this research that the control strategies work well and thus the infective population sizes of both asymptomatic and symptomatic classes reduce drastically within a short period of time. Also, the analysis of cost-effectiveness is depicted. Finally, based upon the simulation values of optimal controls, the combination of Prevention, Treatment and Screening of infectious humans is the most efficient and less costly strategy to eradicate pneumonia diseases from the community.

Pneumonia diseases, SPIaIsRsR model, Optimal control, cost-effectiveness analysis