Optimal switching strategies in multidrug therapies for chronic diseases.

Antimicrobial resistance is a threat to public health with millions of deaths linked to drug-resistant infections every year. To mitigate resistance, common strategies that are used are combination therapies and therapy switching. However, the stochastic nature of pathogenic mutation makes the optimization of these strategies challenging. Here, we propose a two-scale stochastic model that considers the effective evolution of therapies in a multidimensional efficacy space, where each dimension represents the efficacy of a specific drug in the therapy. The diffusion of therapies within this space is subject to stochastic resets, representing therapy switches. The boundaries of the space, inferred from coarser pathogen-host dynamics, can be either reflecting or absorbing. Reflecting boundaries impede full recovery of the host, while absorbing boundaries represent the development of antimicrobial resistance, leading to therapy failure. We derive analytical expressions for the average absorption times, accounting for both continuous and discrete genomic changes using the frameworks of Langevin and master equations, respectively. These expressions allow us to evaluate the relevance of times between drug switches and the number of simultaneous drugs in relation to typical timescales for drug resistance development. To study realistic therapy scenarios, we impose constraints on the number of administered therapies and/or their costs, which reveals nontrivial optimal drug-switching protocols that maximize the time before antimicrobial resistance develops while reducing therapy costs. Finally, we extend the model to consider single-cell heterogeneity to accurately capture the effects of individual mutations that result in drug resistance.