Estimating epidemic parameters: Application to H1N1 pandemic data

Schwartz, Ernest; Choi, Boseung; Rempała, Grzegorz A.

doi:10.1016/j.mbs.2015.03.007

Cited by 19 publications

(17 citation statements)

References 23 publications

(34 reference statements)

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“…However, many questions persist. Schwartz et al [171] study the average number of secondary influenza virus infections, which does not match observations, when it is estimated via maximum likelihood estimation (MLE). By contrast, when the fitting is done with least-squares estimation (LSE), the calculation of secondary infections performs better.…”

Section: Scale-bridging Modeling Approachesmentioning

confidence: 99%

From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

Gutiérrez

Galinski

Cantrell

et al. 2015

Mathematical Biosciences

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Since their earliest days, humans have been struggling with infectious diseases. Caused by viruses, bacteria, protozoa, or even higher organisms like worms, these diseases depend critically on numerous intricate interactions between parasites and hosts, and while we have learned much about these interactions, many details are still obscure. It is evident that the combined host-parasite dynamics constitutes a complex system that involves components and processes at multiple scales of time, space, and biological organization. At one end of this hierarchy we know of individual molecules that play crucial roles for the survival of a parasite or for the response and survival of its host. At the other end, one realizes that the spread of infectious diseases by far exceeds specific locales and, due to today's easy travel of hosts carrying a multitude of organisms, can quickly reach global proportions. The community of mathematical modelers has been addressing specific aspects of infectious diseases for a long time. Most of these efforts have focused on one or two select scales of a multi-level disease and used quite different computational approaches. This restriction to a molecular, physiological, or epidemiological level was prudent, as it has produced solid pillars of a foundation from which it might eventually be possible to launch comprehensive, multi-scale modeling efforts that make full use of the recent advances in biology and, in particular, the various high-throughput methodologies accompanying the emerging –omics revolution. This special issue contains contributions from biologists and modelers, most of whom presented and discussed their work at the workshop From within Host Dynamics to the Epidemiology of Infectious Disease, which was held at the Mathematical Biosciences Institute at Ohio State University in April 2014. These contributions highlight some of the forays into a deeper understanding of the dynamics between parasites and their hosts, and the consequences of this dynamics for the spread and treatment of infectious diseases.

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Section: Scale-bridging Modeling Approachesmentioning

confidence: 99%

From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

Gutiérrez

Galinski

Cantrell

et al. 2015

Mathematical Biosciences

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“…In the autumn of 2009, a new strain of influenza spread around the world after its initial outbreak in the state of Veracruz, Mexico in April 2009. The influenza A(H1N1)pdm09 virus was a triple reassortment of bird, swine and human flu viruses further combined with a Eurasian pig influenza virus [38]. Unlike most strains of influenza, this influenza A(H1N1) virus did not disproportionately infect adults older than 60 years, and it spread easily among young, healthy adults.…”

Section: Discussionmentioning

confidence: 99%

“…Assuming r individuals have recovered after infectious periods w 1 < · · · < w r < T , we have ℓRfalse(w1,…,wrfalsefalse|θ,kfalse)=false(k−rfalse)log⁡Hγfalse(Tfalse)+∑i=1rlog⁡hγfalse(wifalse),where Hγfalse(⋅false) and hγfalse(⋅false) are, respectively, the survival function and the probability density function of the exponential distribution with rate γ . Averaging the infectious periods used in the previous analysis [38,39], we assume here that the recovery times have an exponential distribution with mean γ −1 = 5.5 days (see also [40,41]), so γ was not estimated. The complete log-likelihood conditional on the population size n , the parameters and observables is then ℓ0(t1…,tk,w1,…,wr|θ,n)=ℓI(t1,…,tk|θ,n)+ℓ…”

Section: Discussionmentioning

confidence: 99%

Survival dynamical systems: individual-level survival analysis from population-level epidemic models

et al. 2019

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In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University.

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“…10,11,14,16,22,30,31 The commonly used mathematical model among all is SIER model as it takes all factors of an epidemic phase of an individual i.e. Susceptible -Exposed -InfectiveRecovered.…”

Section: Totalmentioning

confidence: 99%

Models to predict H1N1 outbreaks: a literature review

Mutalik¹

2017

Int J Community Med Public Health

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With high mortality and panic association, policy-makers face the difficult task of making appropriate and timely decisions to mitigate the serious adverse effects over a short period of time during H1N1 influenza outbreak. Mathematical models predict the number of the cases and thus provide an insight for preparedness during outbreak. The objective was to identify various mathematical models used in prediction of H1N1 outbreaks till date and to compare the usefulness of these models in providing magnitude of H1N1 outbreaks. Hence a secondary data analysis of literature review was done. The literature search was conducted using PubMed and Google scholar, restricting it to articles published until May 2015. The key parameters were set for selection of articles and hence a total of 31 articles has been reviewed. Of each article included in the review, the following data was recorded: year of the study, year of pandemic referring to, country, described mathematical model with results of study The SEIR model is most commonly used mathematical model. SIER model takes all factors in a epidemic phase of an individual i.e. Susceptible -Exposed -Infective -Recovered. While studies which utilised SIER model with the combination of other models found the other factors which influence the occurrence of H1N1 outbreaks and also helped in prediction and prevention of number of cases during outbreak. The SEIR models in combination utilised secondary models such as social networking, global network and total layered containment. The literature review suggests that probable use of mathematical model along with some secondary models will help in better prediction and prevention of number of cases during outbreak.

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Estimating epidemic parameters: Application to H1N1 pandemic data

Cited by 19 publications

References 23 publications

From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges

Survival dynamical systems: individual-level survival analysis from population-level epidemic models

Models to predict H1N1 outbreaks: a literature review

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