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INTERIOR Estimates OF SEMIDISCRETE FINITE ELEMENT METHODS FOR PARABOLIC PROBLEMS WITH DISTRIBUTIONAL DATA

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Journal of Computational Mathematics 2019年第4期37卷 458-474页

作者： Li Guo Hengguang Li Yang Yang School of Data and Computer Science Sun Yat-Sen University Guangzhou 510275 China Department of Mathematics Wayne State University Michigan 48202 USA Department of Mathematical Sciences Michigan Technological University Michigan USA

Let Ω CR^d,1≤d≤3, be a bounded d-polytope. Consider the parabolic equation on Q with the Dirac delta function on the right hand side. We study the well-posedness, regularity, and the interior error estimate of semidiscrete finite element approximations of the equation. In particular, we derive that the interior error is bounded by the best local approximation error, the negative norms of the error, and the negative norms of the time derivative of the error. This result implies different convergence rates for the numerical solution in different interior regions, especially when the region is close to the singular point. Numerical test results are reported to support the theoretical prediction.

关键词： Parabolic problems Dist ributional data Finite element met hods Interior Estimates Well-posedness Singularity

Hydrological Simulation Using TRMM and CHIRPS Precipitation Estimates in the Lower Lancang-Mekong River Basin

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Chinese Geographical Science 2019年第1期29卷 13-25页

作者： LUO Xian WU Wenqi HE Daming LI Yungang JI Xuan Asian International Rivers Center Yunnan University Yunnan Key Laboratory of International Rivers and Transboundary Eco-security

Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall stations are sparse and unevenly distributed, and the transboundary characteristic makes the collection of precipitation data more difficult, which has restricted hydrological processes simulation. In this study, daily precipitation data from four datasets(gauge observations, inverse distance weighted(IDW) data, Tropical Rainfall Measuring Mission(TRMM) Estimates, and Climate Hazards Group InfraRed Precipitation with Stations(CHIRPS) Estimates), were applied to drive the Soil and Water Assessment Tool(SWAT) model, and then their capability for hydrological simulation in the Lower Lancang-Mekong River Basin were examined. TRMM and CHIRPS data showed good performances on precipitation estimation in the Lower Lancang-Mekong River Basin, with the better performance for TRMM product. The Nash-Sutcliffe efficiency(NSE) values of gauge, IDW, TRMM, and CHIRPS simulations during the calibration period were 0.87, 0.86, 0.95, and 0.93 for monthly flow, respectively, and those for daily flow were 0.75, 0.77, 0.86, and 0.84, respectively. TRMM and CHIRPS data were superior to rain gauge and IDW data for driving the hydrological model, and TRMM data produced the best simulation performance. Satellite-based precipitation Estimates could be suitable data sources when simulating hydrological processes for large data-poor or ungauged watersheds, especially in international river basins for which precipitation observations are difficult to collect. CHIRPS data provide long precipitation time series from 1981 to near present and thus could be used as an alternative precipitation input for hydrological simulation, especially for the period without TRMM data. For satellite-based precipitation products, the differences in the occurrence frequencies and amounts of precipitation with different intensities would affect simulation re

关键词： hydrological simulation satellite-based precipitation Estimates spatial distribution of precipitation international river the Lower Lancang-Mekong River Basin

Improving Estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework

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Infectious Disease Modelling 2023年第4期8卷 1127-1137页

作者： Punya Alahakoon James M.McCaw Peter GTaylor School of Mathematics and Statistics The University of MelbourneMelbourneAustralia Centre for Epidemiology and Biostatistics Melbourne School of Population and Global HealthThe University of MelbourneMelbourneAustralia School of Population Health University of New South WalesSydneyAustralia Kirby Institute University of New South WalesSydneyAustralia

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual,continued persistence of the pathogen within the population requires the replenishment of susceptibles through births,immigration,or waning immunity.Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection.If,initially,the prevalence of disease increases(that is,the infection takes off),the number of infectives will usually decrease to a low level after the first major outbreak.During this post-outbreak period,the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out.Die out in this period following the first major outbreak is known as an epidemic fade-out.If the disease does not die out,the susceptible population may be replenished by the waning of immunity,and a second wave may start.In this study,we investigate if the rate of waning immunity(and other epidemiological parameters)can be reliably estimated from multiple outbreak data,in which some outbreaks display epidemic fade-out and others do not.We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities.Some outbreaks faded-out and some did not.We conducted Bayesian parameter estimation under two alternative approaches:independently on each outbreak and under a hierarchical framework.When conducting independent estimation,the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed.However,under a hierarchical approach,we obtained more accurate and precise posterior Estimates for the rate of waning immunity and other epidemiological parameters.The greatest improvement in Estimates was obtained for those communities in which epidemic fade-out was observed.

关键词： Estimates stochastic estimation

具有一般非线性耦合项的抛物型方程组的爆破时间估计

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Chinese Quarterly Journal of Mathematics 2020年第1期35卷 77-92页

作者：胡彩华李锋杰王千喜 College of Science China University of PetroleumQingdao 266580

This paper deals with some parabolic equations,where the reaction and the boundary flux are taken of some general forms.We study the explicit blow-up time Estimates according to the different coupled relationship,including the lower and upper bounds of blow-up time for every dimension of space domains.As examples,the results could be used to so many completely coupled models.

关键词： parabolic equations general coupled nonlinearity boundary flux blow-up time Estimates

GLOBAL EXISTENCE AND POINTWISE Estimates OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS

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Acta Mathematica Scientia 2019年第1期39卷 180-194页

作者：张颖妹李朗房少梅 Department of Mathematics South China Agricultural University

The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy Estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.

关键词： Kuramoto-Sivashinsky equation global existence pointwise Estimates Green’s function method energy method

Inequality Estimates of an Inhomogeneous Semilinear Biharmonic Equation in Entire Space

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 812-819页

作者： Fen YANG Department of Mathematics and Statistics Wuhan University of Science and Technology

In this paper,we consider the inequality Estimates of the positive solutions for the inhomogeneous biharmonic equation■-△^2u+u^p+f(x)=0 in R^n where △^2 is the biharmonic operator,p>1,n≥5 and 0≡f∈C(R^n)is a given nonnegative function.We obtain different inequality Estimates of Eq.(*),with which the necessary conditions of existence on f and p are also established.

关键词： inhomogeneous biharmonic equation positive solution inequality Estimates

Modelling the Impact of Stages of HIV Progression on Estimates

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Advances in Infectious Diseases 2015年第3期5卷 101-113页

作者： Angelina Mageni Lutambi Ifakara Health Institute Dar es Salaam Tanzania

HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model Estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different Estimates, with the model without stages producing lower Estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.

关键词： HIV Stages Transmission Mathematical Model Population Dynamics Model Estimates

Error Estimates for the Difference Method to System of Ordinary Differential Equations with Boundary Layer

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Journal of Applied Mathematics and Physics 2013年第5期1卷 79-84页

作者： Ilhame Amirali Department of Mathematics Faculty of Art and Science Sinop University Sinop Turkey

This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a unifo... 详细信息

关键词： Singular Perturbation Linear System Difference Scheme Uniform Convergence Error Estimates

Proportionate Target Population Estimates Used by National Immunization Programmes in Sub-Saharan Africa and Comparison with Values from an External Source

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World Journal of Vaccines 2014年第3期4卷 147-156页

作者： David W. Brown Anthony H. Burton Marta Gacic Dobo Richard Mihigo The World Health Organization Regional Office for Africa Brazzaville Republic of Congo The World Health Organization Geneva Switzerland United Nations Children’s Fund New York USA

Background: In order to effectively plan the delivery of immunization services, manage stock and supply levels and target interventions, national immunization programmes (NIP) must have an estimate of the target population they serve. To overcome challenges with target population estimation, some NIPs apply “rule-of-thumb” conversion factors to total population Estimates. We compare these proportionate target population values with those from an external source. Methods: Using data reported by national immunization programmes in sub-Saharan Africa, we computed the proportionate target population as the number of births, surviving infants and children under 5 years of age, respectively, as a proportion of the total population size. We compared these values with those Estimates computed from United Nations Population Division (UNPD) data. We then recomputed NIP target population sizes using the proportionate target population values from the UNPD applied to the total population size reported by NIP. Results: Data were available from 47 sub-Saharan Africa countries. Births as a proportion of the total population were greater within reports from NIP (median, 0.0400;IQR: 0.350 - 0.0437) compared to values from UNPD Estimates (median, 0.0364;IQR: 0.0332 - 0.0406). Similar patterns were observed for surviving infants (median: NIP, 0.0360;UNPD, 0.0337) and children under 5 years of age (median: NIP, 0.1735;UNPD, 0.1594). The percent difference in proportionate target population ratios between reports from NIPs and the UNPD was >10% in 23 countries for births, in 18 countries for surviving infants, in 15 countries for children under 5 years of age. After re-computing target populations using UNPD proportionate target population values applied to NIP reported total population, recomputed administrative coverage levels for the third dose of DTP containing vaccine were higher in 32 of the 47 countries compared to reported administrative coverage levels. Conclusion: Because childhood immunization-related target populations ar

关键词： Population Population Estimates Target Population Immunization Immunization Coverage