TITLE:
Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables
AUTHORS:
Muhammad Altaf Khan, Gul Zaman, Saeed Islam, Muhammad Ikhlaq Chohan
KEYWORDS:
Mathematical Model; Optimal Control; Pontryagin’s Maximum Principle; Numerical Results
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.11,
November
20,
2012
ABSTRACT: In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.