Simulation-optimization framework for the digital design of pharmaceutical processes using Pyomo and PharmaPy.

The problem of performing model-based process design and optimization in the pharmaceutical industry is an important and challenging one both computationally and in choice of solution implementation. In this work, a framework is presented to directly utilize a process simulator via callbacks during derivative-based optimization. The framework allows users with little experience in translating mechanistic ODEs and PDEs to robust, fully discretized algebraic formulations, required for executing simultaneous equation-oriented optimization, to obtain mathematically guaranteed optima at a competitive solution time when compared with existing derivative-free and derivative-based frameworks. The effectiveness of the framework in accuracy of optimal solution as well as computational efficiency is analyzed on on two case studies: (i) an integrated 2-unit reaction synthesis train used for the synthesis of an anti-cancer active pharmaceutical ingredient, and (ii) a more complex flowsheet representing a common synthesis-purification-isolation train of a pharmaceutical manufacturing processes.

Evaluating Manual Sampling Locations for Regulatory and Emergency Response.

Drinking water systems commonly use manual or grab sampling to monitor water quality, identify or confirm issues, and verify that corrective or emergency response actions have been effective. In this paper, the effectiveness of regulatory sampling locations for emergency response is explored. An optimization formulation based on the literature was used to identify manual sampling locations to maximize overall nodal coverage of the system. Results showed that sampling locations could be effective in confirming incidents for which they were not designed. When evaluating sampling locations optimized for emergency response against regulatory scenarios, the average performance was reduced by 3%-4%, while using optimized regulatory sampling locations for emergency response reduced performance by 7%-10%. Secondary constraints were also included in the formulation to ensure geographical and water age diversity with minimal impact on the performance. This work highlighted that regulatory sampling locations provide value in responding to an emergency for these networks.

Effect of specific non-pharmaceutical intervention policies on SARS-CoV-2 transmission in the counties of the United States.

Non-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (Reff) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median Reff below 1 when combined with either stay at home orders (median Reff 0.97, 95% confidence interval (CI) 0.58-1.39) or face masks (median Reff 0.97, 95% CI 0.58-1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

Interior-point methods for estimating seasonal parameters in discrete-time infectious disease models.

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.

A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model.

Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.