TOP (Treatment Optimiser) consists of Matlab codes that implements algorithms to solve optimal control problems in the context of treatment optimization.
Finding optimal treatment strategies is a very important and non-trivial problem. A policy maker has to take into account a number of factors such as the health state of the patient, resource (monetary) constraints, constraints on the design of a treatment strategy etc.. In our work (Duwal et al. 2015), we presented and compared two treatment paradigms: diagnostic-guided and a pro-active treatment strategies exemplified for controlling HIV-1 replication in the light of resource constraints and evolutionary dynamics of drug resistance development. A diagnostic-guided strategy tailors treatment decisions on an individual basis guided by infrequent and possibly costly diagnostics. In contrast, a pro-active strategy suggests treatment decisions based on experience and projected outcomes. The latter allows switching treatments before drug resistance is detectable, in contrast to a diagnostic-guided strategy. However, pro-actively switching treatments may also lead to unnecessary treatment changes.
Mathematically, a diagnostic-guided strategy can be formulated as a closed-loop optimal control problem and the optimal solution can be efficiently solved using dynamical programming, e.g. by the policy iteration algorithm (Winkelmann et al. 2014). A pro-active strategy can be described as an open-loop optimal control problem. We developed an efficient dynamic programming algorithm based on a branch-and-bound technique (Duwal et al. 2015) allowing to solve this optimization problem efficiently.
-) Optimal treatment strategies in the context of ‘treatment for prevention’ against HIV-1 in resource-poor settings. S. Duwal, S. Winkelmann, C. Schütte and M. von Kleist, PLoS Comput. Biol., 11, e1004200, 2015
-) Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1 S. Winkelmann, C. Schütte and M. von Kleist. Communications in Mathematical Sciences 12, 859, 2014
Graphics comparing Pro-active and Diagnostic guided Strategies