30,415 research outputs found
Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer
Adoptive Cell Transfer therapy of cancer is currently in full development and
mathematical modeling is playing a critical role in this area. We study a
stochastic model developed by Baar et al. in 2015 for modeling immunotherapy
against melanoma skin cancer. First, we estimate the parameters of the
deterministic limit of the model based on biological data of tumor growth in
mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic
Approximation Expectation Maximization algorithm. With the estimated
parameters, we head back to the stochastic model and calculate the probability
that the T cells all get exhausted during the treatment. We show that for some
relevant parameter values, an early relapse is due to stochastic fluctuations
(complete T cells exhaustion) with a non negligible probability. Then, focusing
on the relapse related to the T cell exhaustion, we propose to optimize the
treatment plan (treatment doses and restimulation times) by minimizing the T
cell exhaustion probability in the parameter estimation ranges.Comment: major reorganisation of the paper and the reformulation of many
substantial part
Optimal vaccination in a stochastic epidemic model of two non-interacting populations
Developing robust, quantitative methods to optimize resource allocations in
response to epidemics has the potential to save lives and minimize health care
costs. In this paper, we develop and apply a computationally efficient
algorithm that enables us to calculate the complete probability distribution
for the final epidemic size in a stochastic Susceptible-Infected-Recovered
(SIR) model. Based on these results, we determine the optimal allocations of a
limited quantity of vaccine between two non-interacting populations. We compare
the stochastic solution to results obtained for the traditional, deterministic
SIR model. For intermediate quantities of vaccine, the deterministic model is a
poor estimate of the optimal strategy for the more realistic, stochastic case.Comment: 21 pages, 7 figure
Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
Approximate Bayesian computation methods can be used to evaluate posterior
distributions without having to calculate likelihoods. In this paper we discuss
and apply an approximate Bayesian computation (ABC) method based on sequential
Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC
SMC gives information about the inferability of parameters and model
sensitivity to changes in parameters, and tends to perform better than other
ABC approaches. The algorithm is applied to several well known biological
systems, for which parameters and their credible intervals are inferred.
Moreover, we develop ABC SMC as a tool for model selection; given a range of
different mathematical descriptions, ABC SMC is able to choose the best model
using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure
Ascent trajectory optimisation for a single-stage-to-orbit vehicle with hybrid propulsion
This paper addresses the design of ascent trajectories for a hybrid-engine, high performance, unmanned, single-stage-to-orbit vehicle for payload deployment into low Earth orbit. A hybrid optimisation technique that couples a population-based, stochastic algorithm with a deterministic, gradient-based technique is used to maximize the nal vehicle mass in low Earth orbit after accounting for operational constraints on the dynamic pressure, Mach number and maximum axial and normal accelerations. The control search space is first explored by the population-based algorithm, which uses a single shooting method to evaluate the performance of candidate solutions. The resultant optimal control law and corresponding trajectory are then further refined by a direct collocation method based on finite elements in time. Two distinct operational phases, one using an air-breathing propulsion mode and the second using rocket propulsion, are considered. The presence of uncertainties in the atmospheric and vehicle aerodynamic models are considered in order to quantify their effect on the performance of the vehicle. Firstly, the deterministic optimal control law is re-integrated after introducing uncertainties into the models. The proximity of the final solutions to the target states are analysed statistically. A second analysis is then performed, aimed at determining the best performance of the vehicle when these uncertainties are included directly in the optimisation. The statistical analysis of the results obtained are summarized by an expectancy curve which represents the probable vehicle performance as a function of the uncertain system parameters. This analysis can be used during the preliminary phase of design to yield valuable insights into the robustness of the performance of the vehicle to uncertainties in the specification of its parameters
A partially linearized sigma point filter for latent state estimation in nonlinear time series models
A new technique for the latent state estimation of a wide class of nonlinear time
series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process
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