A stochastic optimization framework for treatment planning with resistance heterogeneity

This paper develops a stochastic optimization framework for treatment planning under heterogeneous and uncertain resistance. Intrinsic variability can be captured in an analytically tractable environment by modeling cellular resistance as a random variable with a beta distribution. Important monotonicity and convexity features are established by deriving and analyzing a closed-form formula for the estimated infection probability. Both static and dynamic formulations utilize these structural results to identify the optimal choices. While comparative statics show that greater resistance consistently delays intervention, detailed dynamic programming analysis in the infinite-horizon context reveals that effective treatment plans exhibit a threshold structure concerning exposure intensity. To bolster the analytical conclusions and demonstrate the strength of the suggested decision criteria, numerical experiments are presented.