Modeling the persistence of Opisthorchis viverrini worm burden after mass-drug administration and education campaigns with systematic adherence.

Opisthorchis viverrini is a parasitic liver fluke contracted by consumption of raw fish, which affects over 10 million people in Southeast Asia despite sustained control efforts. Chronic infections are a risk factor for the often fatal bile duct cancer, cholangiocarcinoma. Previous modeling predicted rapid elimination of O. viverrini following yearly mass drug administration (MDA) campaigns. However, field data collected in affected populations shows persistence of infection, including heavy worm burden, after many years of repeated interventions. A plausible explanation for this observation is systematic adherence of individuals in health campaigns, such as MDA and education, with some individuals consistently missing treatment. We developed an agent-based model of O. viverrini which allows us to introduce various heterogeneities including systematic adherence to MDA and education campaigns at the individual level. We validate the agent-based model by comparing it to a previously published population-based model. We estimate the degree of systematic adherence to MDA and education campaigns indirectly, using epidemiological data collected in Lao PDR before and after 5 years of repeated MDA, education and sanitation improvement campaigns. We predict the impact of interventions deployed singly and in combination, with and without the estimated systematic adherence. We show how systematic adherence can substantially increase the time required to achieve reductions in worm burden. However, we predict that yearly MDA campaigns alone can result in a strong reduction of moderate and heavy worm burden, even under systematic adherence. We predict latrines and education campaigns to be particularly important for the reduction in overall prevalence, and therefore, ultimately, elimination. Our findings show how systematic adherence can explain the observed persistence of worm burden; while emphasizing the benefit of interventions for the entire population, even under systematic adherence. At the same time, the results highlight the substantial opportunity to further reduce worm burden if patterns of systematic adherence can be overcome.

Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM.

Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to compute a random domain mapping on the whole domain, such that the domain mapping is the identity on the fixed subdomain and maps the boundary of the chosen fixed, nominal domain on to the random boundary. To overcome the necessity of computing such a mapping, we therefore couple the finite element method on the fixed subdomain with the boundary element method on the random boundary. We verify on one hand the regularity of the solution with respect to the random domain mapping required for many multilevel quadrature methods, such as the multilevel quasi-Monte Carlo quadrature using Halton points, the multilevel sparse anisotropic Gauss-Legendre and Clenshaw-Curtis quadratures and multilevel interlaced polynomial lattice rules. On the other hand, we derive the coupling formulation and show by numerical results that the approach is feasible.

Frames for the Solution of Operator Equations in Hilbert Spaces with Fixed Dual Pairing.

For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are not identified. This means that the Riesz isomorphism is not used as an identification, which, for example, does not make sense for the Sobolev spaces H 0 1 ( Ω ) and H - 1 ( Ω ) . In this article, we are going to revisit the concept of Stevenson frames and introduce it for Banach spaces. This is equivalent to ℓ 2 -Banach frames. It is known that, if such a system exists, by defining a new inner product and using the Riesz isomorphism, the Banach space is isomorphic to a Hilbert space. In this article, we deal with the contrasting setting, where H and H ' are not identified, and equivalent norms are distinguished, and show that in this setting the investigation of ℓ 2 -Banach frames make sense.

Boosting Quantum Machine Learning Models with a Multilevel Combination Technique: Pople Diagrams Revisited.

Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multilevel combination (C) technique, to combine various levels of approximations made when molecular energies are calculated. When combined with quantum machine learning (QML) models, the resulting CQML model is a generalized unified recursive kernel ridge regression that exploits correlations implicitly encoded in training data composed of multiple levels in multiple dimensions. Here, we have investigated up to three dimensions: chemical space, basis set, and electron correlation treatment. Numerical results have been obtained for atomization energies of a set of ∼7000 organic molecules with up to 7 atoms (not counting hydrogens) containing CHONFClS, as well as for ∼6000 constitutional isomers of C7H10O2. CQML learning curves for atomization energies suggest a dramatic reduction in necessary training samples calculated with the most accurate and costly method. In order to generate millisecond estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors reaching chemical accuracy (∼1 kcal/mol), the CQML model requires only ∼100 training instances at CCSD(T)/cc-pvdz level, rather than thousands within conventional QML, while more training molecules are required at lower levels. Our results suggest a possibly favorable trade-off between various hierarchical approximations whose computational cost scales differently with electron number.

Analysis of interventions against the liver fluke, opisthorchis viverrini.

We adapt a population-based model of Opisthorchis viverrini transmission dynamics to determine the effectiveness of three different interventions. The model includes the definitive hosts, humans; the reservoir hosts, dogs and cats; and the intermediate hosts, snails and fish. We consider the interventions: education campaigns to reduce the consumption of raw or undercooked fish, improved sanitation and treatment through mass drug administration. We fit model parameters to a data set from two islands in southern Lao PDR. We calculate the control reproduction number, simulate different scenarios and optimise the interventions with optimal control. We look at the potential of the interventions to eliminate transmission within 20 years. The model shows that education and improved sanitation need a very high coverage to fulfil the goal of elimination, whereas annual drug distribution at medium coverage is sufficient. The best solution is a combination of drug distribution at a medium level of coverage and as high as possible coverage of education and improved sanitation.

Mathematical analysis of the transmission dynamics of the liver fluke, Opisthorchis viverrini.

We develop and analyse two population-based models of the transmission dynamics of the worm parasite Opisthorchis viverrini. The life cycle of O. viverrini includes humans, cats and dogs as definitive hosts; and snails and fish as intermediate hosts. The first model has only one definitive host (humans) while the second model has two additional hosts: the reservoir hosts, cats and dogs. We define reproduction numbers and endemic equilibrium points for the two models. We use prevalence data for the five hosts from two islands in Lao People's Democratic Republic to estimate distributions of parameter values. We use these distributions to compute the sensitivity index and the partial rank correlation coefficient of the basic reproduction number and the endemic equilibrium point to the parameters. We calculate distributions of the host-specific type-reproduction number to show that humans are necessary to maintain transmission and can sustain transmission without additional reservoir hosts. Therefore interventions targeting humans could be sufficient to interrupt transmission of O. viverrini.

Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements.

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the integral equation formulation (IEF) of the polarizable continuum model (PCM), generally lead to working equations which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort.

Wavelet formulation of the polarizable continuum model.

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF-PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N(1.5) scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used.