EEA algorithm model in estimating spread and evaluating countermeasures on high performance computing

This work started out with the in-depth feasibil-ity study and limitation analysis on the current disease spread estimating and countermea-sures evaluating models, then we identify that the population variability is a crucial impact which has been always ignored or less empha-sized. Taking HIV/AIDS as the application and validation background, we propose a novel al-gorithm model system, EEA model system, a new way to estimate the spread situation, evaluate different countermeasures and analyze the development of ARV-resistant disease strains. The model is a series of solvable ordi-nary differential equation (ODE) models to es-timate the spread of HIV/AIDS infections, which not only require only one year’s data to deduce the situation in any year, but also apply the piecewise constant method to employ multi- year information at the same time. We simulate the effects of therapy and vaccine, then evaluate the difference between them, and offer the smallest proportion of the vaccination in the population to defeat HIV/AIDS, especially the advantage of using the vaccination while the deficiency of using therapy separately. Then we analyze the development of ARV-resistant dis-ease strains by the piecewise constant method. Last but not least, high performance computing (HPC) platform is applied to simulate the situa-tion with variable large scale areas divided by grids, and especially the acceleration rate will come to around 4 to 5.5.

Error Estimation and Assessment of an Approximation in a Wavelet Collocation Method

This article describes how to assess an approximation in a wavelet collocation method which minimizes the sum of squares of residuals. In a research project several different types of differential equations were approximated with this method. A lot of parameters must be adjusted in the discussed method here. For example one parameter is the number of collocation points. In this article we show how we can detect whether this parameter is too small and how we can assess the error sum of squares of an approximation. In an example we see a correlation between the error sum of squares and a criterion to assess the approximation.

A vaccination model for COVID-19 in Gauteng,South Africa

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection,and we investigate these strategies in early-stage outbreak dynamics.The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies.Using a system of ordinary differential equations,we model the outbreak in the province of Gauteng,assuming that several parameters vary over time.Analyzing data from the time period before vaccination gives the approximate dates of parameter changes,and those dates are linked to government policies.Unknown parameters are then estimated from available case data and used to assess the impact of each policy.Looking forward in time,possible scenarios give projections involving the implementation of two different vaccines at varying times.Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Asymptotic expansions of complete Kahler-Einstein metrics with finite volume on quasi-projective manifolds

We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-projective manifolds.The main tools are the solution formula for second-order ordinary differential equations(ODEs)with constant coefficients and spectral theory for the Laplacian operator on a closed manifold.