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We provide easy and readable GNU Octave/MATLAB code for the simulation ofmathematical models described by ordinary differential equations and for thesolution of optimal control problems through Pontryagin's maximum principle.For that, we consider a normalized HIV/AIDS transmission dynamics model basedon the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. ASICA compartmental model in epidemiology with application to HIV/AIDS in CapeVerde. Ecol. Complex. 2017, 30, 70--75), given by a system of four ordinarydifferential equations. An HIV initial value problem is solved numericallyusing the ode45 GNU Octave function and three standard methods implemented byus in Octave/MATLAB: Euler method and second-order and fourth-order Runge-Kuttamethods. Afterwards, a control function is introduced into the normalized HIVmodel and an optimal control problem is formulated, where the goal is to findthe optimal HIV prevention strategy that maximizes the fraction of uninfectedHIV individuals with the least HIV new infections and cost associated with thecontrol measures. The optimal control problem is characterized analyticallyusing the Pontryagin Maximum Principle, and the extremals are computednumerically by implementing a forward-backward fourth-order Runge-Kutta method.Complete algorithms, for both uncontrolled initial value and optimal controlproblems, developed under the free GNU Octave software and compatible withMATLAB are provided along the article.

Numerical Optimal Control of HIV Transmission in Octave/MATLAB