Abstract
A mathematical model based on ordinary differential equations to study AIDS dynamics at a population level and giving importance to diagnosis of infected is proposed. Five populations are considered: susceptibles, healthy diagnosed, healthy undiagnosed HIV positives, sick diagnosed, and undiagnosed HIV positives. The number R 0 is analytically calculated and used in numerical results interpretation to determine the long-term population behavior and which parameters are the most influential on the dynamics. Subsequently, antiviral treatment is incorporated into the model as a control strategy and the Pontryagin maximum principle is used to find out an optimal control function. Finally, different simulations are performed and interpreted.
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Trujillo-Salazar, C., Toro-Zapata, H. (2015). Simulation Model for AIDS Dynamics and Optimal Control Through Antiviral Treatment. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_18
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DOI: https://doi.org/10.1007/978-3-319-12583-1_18
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