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■Bio-mathematics, Statistics and Nano-Technologies: Mosquito Control Strategies
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time t (in days)
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time t (in days)
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b=0.75 and J2
(b) Infectious humans for J1 and J2.
Figure 7.1: Susceptible and infectious individuals for different cost functions J1 and J2
(parameter/constant values from Table 7.1 and b = 0.75).
7.4
NUMERICAL RESULTS AND DISCUSSION
Our numerical results were obtained and confirmed following different approaches.
The first approach consisted in using IPOPT [53] and the algebraic modeling language
AMPL [7].
In a second approach, we used the PROPT Matlab Optimal Control Software [52].
The results were coincident and are easily confirmed by the ones obtained using an itera-
tive method that consists in solving the system of eight ODEs given by (7.1) and (7.A.5)
in Appendix 7.A. For that, one first solves system (7.1) with a guess for the control
over the time interval [0,tf] using a forward fourth-order Runge–Kutta scheme and the
transversality conditions (7.A.4) in Appendix 7.A.
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time t (in days)
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b=0.75 and J2
(a) Susceptible mosquitos for J1 and J2.
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time t (in days)
b=0.75 and J1
b=0.75 and J2
(b) Infectious mosquitos for J1 and J2.
Figure 7.2: Susceptible and infectious mosquitos for different cost functions J1 and J2
(parameter/constant values from Table 7.1 and b = 0.75).