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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.
Highlights
Leptospirosis disease is a globally zoonotic disease
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
We introduced optimal control campaign to the model to maximize the population of recovered human and minimize the population of susceptible and infected human and total vector population using three control variables
Summary
Human as well as cattle are mostly infected from this disease. The human whose urine is used by other animals and cattle are infected, because the leptospirosis germs come out in urine. It is reported that people belong to city are mostly infected from this disease and got liver infection. The infections can be mild and without obvious symptom [2,3,4,5,6]. Outbreaks of this disease depending on season which often linked to environmental factors involve animals, agricultural and occupational cycles [7]
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