SHEPHERD: Markov Decision Processes on Wright–Fisher Dynamics to Mitigate Therapeutic Resistance in Evolving Populations

Therapeutic resistance emerges from stochastic evolutionary dynamics in genetically heterogeneous populations, posing a central challenge in cancer and infectious disease treatment. We introduce the SHEPHERD protocol (Stochastic Heterogeneity–informed Evolutionary Policy Hampering the Expansion of Resistance to Drugs), which integrates Wright–Fisher population genetics with Markov decision processes (MDPs) to compute optimal drug policies that minimize long-term population fitness, thereby reducing resistance. SHEPHERD couples a diffusion approximation of Wright–Fisher dynamics with a simplex-to-hypercube coordinate transformation, followed by a lattice discretization that enables numerically tractable policy optimization. On synthetic multi-drug fitness landscapes with 3, 4, and 8 genotypes, SHEPHERD maintains substantially lower mean fitness than any constant or periodic two-drug regimen. Sensitivity analyses reveal convergence at moderate resolution in genotype-frequency space, but a strong dependence on the drug-update interval, underscoring the importance of rapid feedback for maintaining control. Our study establishes a foundation for applying MDP-based optimization to stochastic evolutionary dynamics, highlighting the opportunities and challenges of steering evolution through drug sequencing.