A comparison of computational efficiencies of stochastic algorithms in terms of two infection models

Exact Variance-Reduced Simulation of Lattice Continuous-Time Markov Chains with Applications in Reaction Networks

We propose an algorithm to reduce the variance of Monte Carlo simulation for the class of countable-state, continuous-time Markov chains, or lattice CTMCs. This broad class of systems includes all processes that can be represented using a random-time-change representation, in particular reaction networks. Numerical studies demonstrate order-of-magnitude reduction in MSE for Monte Carlo mean estimates using our approach for both linear and nonlinear systems. The algorithm works by simulating pairs of negatively correlated, identically distributed sample trajectories of the stochastic process and using them to produce variance-reduced, unbiased Monte Carlo estimates, effectively generalizing the method of antithetic variates into the domain of stochastic processes. We define a method to simulate anticorrelated, unit-rate Poisson process paths. We then show how these antithetic Poisson process pairs can be used as the input for random time-change representations of any lattice CTMC, in order to produce anticorrelated trajectories of the desired process. We present three numerical parameter studies. The first examines the algorithm's performance for the unit-rate Poisson process, and the next two demonstrate the effectiveness of the algorithm in simulating reaction network systems: a gene expression system with affine rate functions and an aerosol particle coagulation system with nonlinear rates. We also prove exact, analytical expressions for the time-resolved and integrated covariance between our antithetic Poisson processes for one technique.

What should be considered if you decide to build your own mathematical model for predicting the development of bacterial resistance? Recommendations based on a systematic review of the literature

Acquired bacterial resistance is one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the spread of resistance and to some extent to control its dynamics. The purpose of this review was to examine existing mathematical models in order to understand the pros and cons of currently used approaches and to build our own model. During the analysis, seven articles on mathematical approaches to studying resistance that satisfied the inclusion/exclusion criteria were selected. All models were classified according to the approach used to study resistance in the presence of an antibiotic and were analyzed in terms of our research. Some models require modifications due to the specifics of the research. The plan for further work on model building is as follows: modify some models, according to our research, check all obtained models against our data, and select the optimal model or models with the best quality of prediction. After that we would be able to build a model for the development of resistance using the obtained results.