DYNAMICAL SYSTEM FOR EBOLA OUTBREAK WITHIN QUARANTINE AND VACCINATION TREATMENTS

Ebola Virus Disease (EVD) is an infectious disease with a high mortality rate which is caused by the virus from the family of Filoviridae, genus of Ebolavirus. Therefore, this research works on the developing model of Ebola disease spread with SLSHVEQIHR type. The purpose of this study is to analyze the spread of Ebola disease with the treatments, which are quarantine and vaccination. Then determine the equilibrium point and basic reproduction number (R0). There are two equilibrium points, the disease free equilibrium point and the endemic equilibrium point. The analysis results in the model show that if R0<1 than the disease free equilibrium point is locally asymptotically stable. If R0>1 than the endemic equilibrium point is locally assymptotically stable. Numerical simulations are performed to show the population dynamics when R0<1and R0>1

Derivative-based Shapley value for global sensitivity analysis and machine learning explainability

We introduce a new Shapley value approach for global sensitivity analysis and machine learning explainability. The method is based on the first-order partial derivatives of the underlying function. The computational complexity of the method is linear in dimension (number of features), as opposed to the exponential complexity of other Shapley value approaches in the literature. Examples from global sensitivity analysis and machine learning are used to compare the method numerically with activity scores, SHAP, and KernelSHAP

SenVis: Interactive Tensor-based Sensitivity Visualization

Sobol's method is one of the most powerful and widely used frameworks for global sensitivity analysis, and it maps every possible combination of input variables to an associated Sobol index. However, these indices are often challenging to analyze in depth, due in part to the lack of suitable, flexible enough, and fast-to-query data access structures as well as visualization techniques. We propose a visualization tool that leverages tensor decomposition, a compressed data format that can quickly and approximately answer sophisticated queries over exponential-sized sets of Sobol indices. This way, we are able to capture the complete global sensitivity information of high-dimensional scalar models. Our application is based on a three-stage visualization, to which variables to be analyzed can be added or removed interactively. It includes a novel hourglass-like diagram presenting the relative importance for any single variable or combination of input variables with respect to any composition of the rest of the input variables. We showcase our visualization with a range of example models, whereby we demonstrate the high expressive power and analytical capability made possible with the proposed method

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Multi-fidelity models are of great importance due to their capability of fusing information coming from different simulations and sensors. Gaussian processes are employed for nonparametric regression in a Bayesian setting. They generalize linear regression embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can augment the inputs with the observations of low-fidelity models in order to learn a more expressive latent manifold and thus increment the model's accuracy. This can be realized recursively with a chain of Gaussian processes with incrementally higher fidelity. We would like to extend these multi-fidelity model realizations to case studies affected by a high-dimensional input space but with low intrinsic dimensionality. In these cases physical supported or purely numerical low-order models are still affected by the curse of dimensionality when queried for responses. When the model's gradient information is provided, the existence of an active subspace, or a nonlinear transformation of the input parameter space, can be exploited to design low-fidelity response surfaces and thus enable Gaussian process multi-fidelity regression, without the need to perform new simulations. This is particularly useful in the case of data scarcity. In this work, we present a new multi-fidelity approach involving active subspaces and nonlinear level-set learning method. We test the proposed numerical method on two different high-dimensional benchmarks, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces.Comment: arXiv admin note: substantial text overlap with arXiv:2010.0834

Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1 and endemic equilibrium tend to asymptotically stable if R0 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control

Resource constraints in an epidemic: a goal programming and mathematical modelling framework for optimal resource shifting in South Africa

The COVID-19 pandemic has had devastating consequences across the globe, and has led many governments into completely new decision making territory. Developing models which are capable of producing realistic projections of disease spread under extreme uncertainty has been paramount for supporting decision making by many levels of government. In South Africa, this role has been fulfilled by the South African COVID-19 Modelling Consortium's generalised Susceptible-ExposedInfectious-Removed compartmental model, known as the National COVID-19 Epi Model. This thesis adapted and contributed to the Model; its primary contribution has been to incorporate the feature that resources available to the health system are limited. Building capacity constraints into the Model allowed it to be used in the resource-scarce context of a pandemic. This thesis further designed and implemented a goal programming framework to shift ICU beds between districts intra-provincially in a way that aimed to minimise deaths caused by the non-availability of ICU beds. The results showed a 15% to 99% decrease in lives lost when ICU beds were shifted, depending on the scenario considered. Although there are limitations to the scope and assumptions of this thesis, it demonstrates that it is possible to combine mathematical modelling with optimisation in a way that may save lives through optimal resource allocation