Mathematical Analysis of Sensitive Parameters on the Dynamical Spread of HIV

Abstract

Sensitivity analysis was performed on a mathematical model of Human Immunodefiency Virus (HIV) to determine the gauge and importance of each parameter to basic reproduction number in the dynamical spread of the disease. The threshold basic reproduction number , 0 R which is the average number of secondary infection generated by infected individuals in his or her infectious period was calculated using next generation matrix method, which shows that, the disease dies out when R0  1, and the disease will persist and spread when 1 0 R  .The relative sensitivity analysis was computed for all the parameters in the basic reproduction number, which shows the influence of each parameter in the dynamical spread of the disease. Numerical sensitivity reveals that effective contact rate and progressor rate are the most sensitive parameters in the basic reproduction number. This analysis will help the medical practitioners and policy health makers to know the best control intervention strategies to be adopted in order to reduce dynamical spread of Human Immunodefiency Virus (HIV) in the community