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Yang T, Wang Y, Yao L, Guo X, Hannah MN, Liu C, Rui J, Zhao Z, Huang J, Liu W, Deng B, Luo L, Li Z, Li P, Zhu Y, Liu X, Xu J, Yang M, Zhao Q, Su Y, Chen T. Application of logistic differential equation models for early warning of infectious diseases in Jilin Province. BMC Public Health 2022; 22:2019. [PMCID: PMC9636661 DOI: 10.1186/s12889-022-14407-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 10/20/2022] [Indexed: 11/06/2022] Open
Abstract
Abstract
Background
There is still a relatively serious disease burden of infectious diseases and the warning time for different infectious diseases before implementation of interventions is important. The logistic differential equation models can be used for predicting early warning of infectious diseases. The aim of this study is to compare the disease fitting effects of the logistic differential equation (LDE) model and the generalized logistic differential equation (GLDE) model for the first time using data on multiple infectious diseases in Jilin Province and to calculate the early warning signals for different types of infectious diseases using these two models in Jilin Province to solve the disease early warning schedule for Jilin Province throughout the year.
Methods
Collecting the incidence of 22 infectious diseases in Jilin Province, China. The LDE and GLDE models were used to calculate the recommended warning week (RWW), the epidemic acceleration week (EAW) and warning removed week (WRW) for acute infectious diseases with seasonality, respectively.
Results
Five diseases were selected for analysis based on screening principles: hemorrhagic fever with renal syndrome (HFRS), shigellosis, mumps, Hand, foot and mouth disease (HFMD), and scarlet fever. The GLDE model fitted the above diseases better (0.80 ≤ R2 ≤ 0.94, P < 0. 005) than the LDE model. The estimated warning durations (per year) of the LDE model for the above diseases were: weeks 12–23 and 40–50; weeks 20–36; weeks 15–24 and 43–52; weeks 26–34; and weeks 16–25 and 41–50. While the durations of early warning (per year) estimated by the GLDE model were: weeks 7–24 and 36–51; weeks 13–37; weeks 11–26 and 39–54; weeks 23–35; and weeks 12–26 and 40–50.
Conclusions
Compared to the LDE model, the GLDE model provides a better fit to the actual disease incidence data. The RWW appeared to be earlier when estimated with the GLDE model than the LDE model. In addition, the WRW estimated with the GLDE model were more lagged and had a longer warning time.
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Li YI, Turk G, Rohrbach PB, Pietzonka P, Kappler J, Singh R, Dolezal J, Ekeh T, Kikuchi L, Peterson JD, Bolitho A, Kobayashi H, Cates ME, Adhikari R, Jack RL. Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19. ROYAL SOCIETY OPEN SCIENCE 2021; 8:211065. [PMID: 34430050 PMCID: PMC8355677 DOI: 10.1098/rsos.211065] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Accepted: 07/23/2021] [Indexed: 06/13/2023]
Abstract
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.
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Affiliation(s)
- Yuting I. Li
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Günther Turk
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Paul B. Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Patrick Pietzonka
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Julian Kappler
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Rajesh Singh
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Jakub Dolezal
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Timothy Ekeh
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Lukas Kikuchi
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Joseph D. Peterson
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Austen Bolitho
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Hideki Kobayashi
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Michael E. Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - R. Adhikari
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Robert L. Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
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3
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Optimal Sampling Regimes for Estimating Population Dynamics. STATS 2021. [DOI: 10.3390/stats4020020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Ecologists are interested in modeling the population growth of species in various ecosystems. Specifically, logistic growth arises as a common model for population growth. Studying such growth can assist environmental managers in making better decisions when collecting data. Traditionally, ecological data is recorded on a regular time frequency and is very well-documented. However, sampling can be an expensive process due to available resources, money and time. Limiting sampling makes it challenging to properly track the growth of a population. Thus, this design study proposes an approach to sampling based on the dynamics associated with logistic growth. The proposed method is demonstrated via a simulation study across various theoretical scenarios to evaluate its performance in identifying optimal designs that best estimate the curves. Markov Chain Monte Carlo sampling techniques are implemented to predict the probability of the model parameters using Bayesian inference. The intention of this study is to demonstrate a method that can minimize the amount of time ecologists spend in the field, while maximizing the information provided by the data.
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Rui J, Luo K, Chen Q, Zhang D, Zhao Q, Zhang Y, Zhai X, Zhao Z, Zhang S, Liao Y, Hu S, Gao L, Lei Z, Wang M, Wang Y, Liu X, Yu S, Xie F, Li J, Liu R, Chiang YC, Zhao B, Su Y, Zhang XS, Chen T. Early warning of hand, foot, and mouth disease transmission: A modeling study in mainland, China. PLoS Negl Trop Dis 2021; 15:e0009233. [PMID: 33760810 PMCID: PMC8021164 DOI: 10.1371/journal.pntd.0009233] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 04/05/2021] [Accepted: 02/11/2021] [Indexed: 11/19/2022] Open
Abstract
BACKGROUND Hand, foot, and mouth disease (HFMD) is a global infectious disease; particularly, it has a high disease burden in China. This study was aimed to explore the temporal and spatial distribution of the disease by analyzing its epidemiological characteristics, and to calculate the early warning signals of HFMD by using a logistic differential equation (LDE) model. METHODS This study included datasets of HFMD cases reported in seven regions in Mainland China. The early warning time (week) was calculated using the LDE model with the key parameters estimated by fitting with the data. Two key time points, "epidemic acceleration week (EAW)" and "recommended warning week (RWW)", were calculated to show the early warning time. RESULTS The mean annual incidence of HFMD cases per 100,000 per year was 218, 360, 223, 124, and 359 in Hunan Province, Shenzhen City, Xiamen City, Chuxiong Prefecture, Yunxiao County across the southern regions, respectively and 60 and 34 in Jilin Province and Longde County across the northern regions, respectively. The LDE model fitted well with the reported data (R2 > 0.65, P < 0.001). Distinct temporal patterns were found across geographical regions: two early warning signals emerged in spring and autumn every year across southern regions while one early warning signals in summer every year across northern regions. CONCLUSIONS The disease burden of HFMD in China is still high, with more cases occurring in the southern regions. The early warning of HFMD across the seven regions is heterogeneous. In the northern regions, it has a high incidence during summer and peaks in June every year; in the southern regions, it has two waves every year with the first wave during spring spreading faster than the second wave during autumn. Our findings can help predict and prepare for active periods of HFMD.
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Affiliation(s)
- Jia Rui
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Kaiwei Luo
- Hunan Provincial Center for Disease Control and Prevention, Changsha City, Hunan Province, People’s Republic of China
| | - Qiuping Chen
- Université de Montpellier, Montpellier, France; CIRAD, Intertryp, Montpellier, France; IES, Université de Montpellier-CNRS, Montpellier, France
- Medical Insurance Office, Xiang’an Hospital of Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Dexing Zhang
- Jockey Club School of Public Health and Primary Care, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, People’s Republic of China
| | - Qinglong Zhao
- Jilin Provincial Center for Disease Control and Prevention, Changchun City, Jilin Province, People’s Republic of China
| | - Yanhong Zhang
- Yunxiao County Center for Disease Control, Zhangzhou City, Fujian Province, People’s Republic of China
| | - Xiongjie Zhai
- Longde County Center for Disease Control, Guyuan City, the Ningxia Hui Autonomous Region, People’s Republic of China
| | - Zeyu Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Siyu Zhang
- Hunan Provincial Center for Disease Control and Prevention, Changsha City, Hunan Province, People’s Republic of China
| | - Yuxue Liao
- Shenzhen Centers for Disease Control and Prevention, Shenzhen City, Guangdong Province, People’s Republic of China
| | - Shixiong Hu
- Hunan Provincial Center for Disease Control and Prevention, Changsha City, Hunan Province, People’s Republic of China
| | - Lidong Gao
- Hunan Provincial Center for Disease Control and Prevention, Changsha City, Hunan Province, People’s Republic of China
| | - Zhao Lei
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Mingzhai Wang
- Xiamen City Center for Disease Control and Prevention, Shenzhen City, Fujian Province, People’s Republic of China
| | - Yao Wang
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Xingchun Liu
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Shanshan Yu
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Fang Xie
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Jia Li
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Ruoyun Liu
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Yi-Chen Chiang
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Benhua Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | - Yanhua Su
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
| | | | - Tianmu Chen
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, People’s Republic of China
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Sumetsky N, Mair C, Wheeler-Martin K, Cerda M, Waller LA, Ponicki WR, Gruenewald PJ. Predicting the Future Course of Opioid Overdose Mortality: An Example From Two US States. Epidemiology 2021; 32:61-69. [PMID: 33002963 PMCID: PMC7708436 DOI: 10.1097/ede.0000000000001264] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
BACKGROUND The rapid growth of opioid abuse and the related mortality across the United States has spurred the development of predictive models for the allocation of public health resources. These models should characterize heterogeneous growth across states using a drug epidemic framework that enables assessments of epidemic onset, rates of growth, and limited capacities for epidemic growth. METHODS We used opioid overdose mortality data for 146 North and South Carolina counties from 2001 through 2014 to compare the retrodictive and predictive performance of a logistic growth model that parameterizes onsets, growth, and carrying capacity within a traditional Bayesian Poisson space-time model. RESULTS In fitting the models to past data, the performance of the logistic growth model was superior to the standard Bayesian Poisson space-time model (deviance information criterion: 8,088 vs. 8,256), with reduced spatial and independent errors. Predictively, the logistic model more accurately estimated fatality rates 1, 2, and 3 years in the future (root mean squared error medians were lower for 95.7% of counties from 2012 to 2014). Capacity limits were higher in counties with greater population size, percent population age 45-64, and percent white population. Epidemic onset was associated with greater same-year and past-year incidence of overdose hospitalizations. CONCLUSION Growth in annual rates of opioid fatalities was capacity limited, heterogeneous across counties, and spatially correlated, requiring spatial epidemic models for the accurate and reliable prediction of future outcomes related to opioid abuse. Indicators of risk are identifiable and can be used to predict future mortality outcomes.
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Affiliation(s)
- Natalie Sumetsky
- Department of Behavioral and Community Health Sciences, University of Pittsburgh Graduate School of Public Health, 130 DeSoto Street, Pittsburgh, PA 15261
| | - Christina Mair
- Department of Behavioral and Community Health Sciences, University of Pittsburgh Graduate School of Public Health, 130 DeSoto Street, Pittsburgh, PA 15261
| | - Katherine Wheeler-Martin
- Center for Opioid Epidemiology and Policy, Division of Epidemiology, Department of Population Health, New York University, 180 Madison Avenue, New York, NY 10016
| | - Magdalena Cerda
- Center for Opioid Epidemiology and Policy, Division of Epidemiology, Department of Population Health, New York University, 180 Madison Avenue, New York, NY 10016
| | - Lance A. Waller
- Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, 1518 Clifton Road NE, Atlanta, GA 30322
| | - William R. Ponicki
- Prevention Research Center, Pacific Institute for Research and Evaluation, 2150 Shattuck Avenue, Suite 601, Berkeley, CA 94704
| | - Paul J. Gruenewald
- Prevention Research Center, Pacific Institute for Research and Evaluation, 2150 Shattuck Avenue, Suite 601, Berkeley, CA 94704
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6
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Lindström HJG, Friedman R. Inferring time-dependent population growth rates in cell cultures undergoing adaptation. BMC Bioinformatics 2020; 21:583. [PMID: 33334308 PMCID: PMC7745411 DOI: 10.1186/s12859-020-03887-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 11/18/2020] [Indexed: 02/08/2023] Open
Abstract
Background The population growth rate is an important characteristic of any cell culture. During sustained experiments, the growth rate may vary due to competition or adaptation. For instance, in presence of a toxin or a drug, an increasing growth rate indicates that the cells adapt and become resistant. Consequently, time-dependent growth rates are fundamental to follow on the adaptation of cells to a changing evolutionary landscape. However, as there are no tools to calculate the time-dependent growth rate directly by cell counting, it is common to use only end point measurements of growth rather than tracking the growth rate continuously. Results We present a computer program for inferring the growth rate over time in suspension cells using nothing but cell counts, which can be measured non-destructively. The program was tested on simulated and experimental data. Changes were observed in the initial and absolute growth rates, betraying resistance and adaptation. Conclusions For experiments where adaptation is expected to occur over a longer time, our method provides a means of tracking growth rates using data that is normally collected anyhow for monitoring purposes. The program and its documentation are freely available at https://github.com/Sandalmoth/ratrack under the permissive zlib license.
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Affiliation(s)
- H Jonathan G Lindström
- Department of Chemistry and Biomedical Sciences, Linnaeus University, 391 82, Kalmar, Sweden
| | - Ran Friedman
- Department of Chemistry and Biomedical Sciences, Linnaeus University, 391 82, Kalmar, Sweden.
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7
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Tesfay A, Tesfay D, Khalaf A, Brannan J. Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise. STOCH DYNAM 2020. [DOI: 10.1142/s0219493721500167] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population [Formula: see text]. In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate [Formula: see text], carrying capacity [Formula: see text], intensity of Gaussian noise [Formula: see text], noise intensity [Formula: see text] and stability index [Formula: see text] vary. The MET from the interval [Formula: see text] at the right boundary is finite if [Formula: see text]. For [Formula: see text], the MET from [Formula: see text] at this boundary is infinite. A larger stability index [Formula: see text] is less likely leading to the extinction of the fish population.
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Affiliation(s)
- Almaz Tesfay
- School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
- Department of Mathematics, Mekelle University, Mekelle, P. O. Box 231, Ethiopia
| | - Daniel Tesfay
- School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
- Department of Mathematics, Mekelle University, Mekelle, P. O. Box 231, Ethiopia
| | - Anas Khalaf
- School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
| | - James Brannan
- Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634, USA
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8
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The study on the early warning period of varicella outbreaks based on logistic differential equation model. Epidemiol Infect 2020; 147:e70. [PMID: 30868977 PMCID: PMC6518620 DOI: 10.1017/s0950268818002868] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Abstract
Chickenpox is a common acute and highly contagious disease in childhood; moreover, there is currently no targeted treatment. Carrying out an early warning on chickenpox plays an important role in taking targeted measures in advance as well as preventing the outbreak of the disease. In recent years, the infectious disease dynamic model has been widely used in the research of various infectious diseases. The logistic differential equation model can well demonstrate the epidemic characteristics of epidemic outbreaks, gives the point at which the early epidemic rate changes from slow to fast. Therefore, our study aims to use the logistic differential equation model to explore the epidemic characteristics and early-warning time of varicella. Meanwhile, the data of varicella cases were collected from first week of 2008 to 52nd week of 2017 in Changsha. Finally, our study found that the logistic model can be well fitted with varicella data, besides the model illustrated that there are two peaks of varicella at each year in Changsha City. One is the peak in summer–autumn corresponding to the 8th–38th week; the other is in winter–spring corresponding to the time from the 38th to the seventh week next year. The ‘epidemic acceleration week’ average value of summer–autumn and winter–spring are about the 16th week (ranging from the 15th to 17th week) and 45th week (ranging from the 44th to 47th week), respectively. What is more, taking warning measures during the acceleration week, the preventive effect will be delayed; thus, we recommend intervene during recommended warning weeks which are the 15th and 44th weeks instead.
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9
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Xuemei H. The indirect method for stochastic logistic growth models. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1019152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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10
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Lanzarone E, Pasquali S, Gilioli G, Marchesini E. A Bayesian estimation approach for the mortality in a stage-structured demographic model. J Math Biol 2017; 75:759-779. [PMID: 28130570 DOI: 10.1007/s00285-017-1099-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Revised: 01/08/2017] [Indexed: 11/28/2022]
Abstract
Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation. This is the case of the extrinsic mortality term that appears in the mortality rate function due to biotic factors. We propose a Bayesian approach to estimate the probability density functions of the parameters in the extrinsic mortality rate function, starting from data on population abundance. The method investigates the time variability in the mortality parameters by comparing simulated and observed trajectories. The grape berry moth, a pest of great importance in European vineyards, has been considered as a case study. Simulated data have been considered to evaluate the convergence of the algorithm, while field data have been used to obtain estimates of the mortality for the grape berry moth.
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Affiliation(s)
- E Lanzarone
- CNR-IMATI, Via A. Corti 12, 20133, Milan, Italy
| | - S Pasquali
- CNR-IMATI, Via A. Corti 12, 20133, Milan, Italy.
| | - G Gilioli
- Department of Molecular and Translational Medicine, University of Brescia, Viale Europa 11, 25123, Brescia, Italy
| | - E Marchesini
- AGREA S.r.l. Centro Studi, Via Garibaldi 5/16, 37057, S. Giovanni Lupatoto (VR), Italy
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11
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Abstract
In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for the existence of stochastic disturbances. Second, for the model, the parameter matrices and noise intensity are obtained. Finally, the simulations of the model show that the subspace identification is more precise than least square method.
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Affiliation(s)
- Miao Yu
- College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China
- State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning 110819, P. R. China
| | - Jianchang Liu
- College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China
- State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning 110819, P. R. China
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12
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Harris EA, Koh EJ, Moffat J, McMillen DR. Automated inference procedure for the determination of cell growth parameters. Phys Rev E 2016; 93:012402. [PMID: 26871096 DOI: 10.1103/physreve.93.012402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2015] [Indexed: 01/01/2023]
Abstract
The growth rate and carrying capacity of a cell population are key to the characterization of the population's viability and to the quantification of its responses to perturbations such as drug treatments. Accurate estimation of these parameters necessitates careful analysis. Here, we present a rigorous mathematical approach for the robust analysis of cell count data, in which all the experimental stages of the cell counting process are investigated in detail with the machinery of Bayesian probability theory. We advance a flexible theoretical framework that permits accurate estimates of the growth parameters of cell populations and of the logical correlations between them. Moreover, our approach naturally produces an objective metric of avoidable experimental error, which may be tracked over time in a laboratory to detect instrumentation failures or lapses in protocol. We apply our method to the analysis of cell count data in the context of a logistic growth model by means of a user-friendly computer program that automates this analysis, and present some samples of its output. Finally, we note that a traditional least squares fit can provide misleading estimates of parameter values, because it ignores available information with regard to the way in which the data have actually been collected.
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Affiliation(s)
- Edouard A Harris
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Canada
| | - Eun Jee Koh
- Department of Molecular Genetics, University of Toronto, 160 College Street, Toronto, Ontario, M5S 3E1, Canada
| | - Jason Moffat
- Department of Molecular Genetics, University of Toronto, 160 College Street, Toronto, Ontario, M5S 3E1, Canada
| | - David R McMillen
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, L5L 1C6, Canada.,Impact Centre, University of Toronto, 112 College Street, Toronto, Ontario, M5G 1A7, Canada
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