Global dynamics of a SEIR model with varying total population size

Li, Michael Y.; Graef, John R.; Wang, Liancheng; Karsai, János

doi:10.1016/s0025-5564(99)00030-9

Cited by 557 publications

(386 citation statements)

References 23 publications

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“…This model (Li et al, 1999) is similar to the previous example, except that recovery is possible, with recovery providing permanent immunity. Thus, there is now a Recovered population class, and there is no flux from the Recovered class to the Susceptible class.…”

Section: Seir Model With Variable Populationmentioning

confidence: 93%

“…Verified Solution of Nonlinear Dynamic Models in Epidemiology 3 of the term βsi for exposure rate is often called simple mass-action incidence (Li et al, 1999) or pseudo mass-action incidence (de Jong, Diekmann and Heesterbeek, 1995).…”

Section: Problem Statementmentioning

confidence: 99%

“…We use the parameter values given by Li et al (1999) a total population of n 0 = 500000 indv with 10% already infected, so i 0 = 50000 indv. The initial populations of the other classes are uncertain and assumed to be s 0 ∈ [400000; 405000] indv, e 0 ∈ [10000; 15000] indv and r 0 ∈ [30000; 40000] indv.…”

Section: Seir Model With Variable Populationmentioning

confidence: 99%

“…Several investigators have focused on a single specific model, computing theoretical bifurcation points as well as some transient and steady-state solutions. This includes work on an SEI model (Pugliese, 1990), an SEIR model (Li, Graef, Wand and Karsai, 1999), and an SEIS model (Fan, Li and Wang, 2001). Models can be either closed or open.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Enszer

Stadtherr

2010

Progress in Industrial Mathematics at ECMI 2008

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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for the verified solution of nonlinear dynamic models we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method used is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

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Section: Seir Model With Variable Populationmentioning

confidence: 93%

Section: Problem Statementmentioning

confidence: 99%

Section: Seir Model With Variable Populationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Enszer

Stadtherr

2010

Progress in Industrial Mathematics at ECMI 2008

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show abstract

“…Using a uniform persistence result from [15] and an argument as in the proof of Proposition 3.3 of Li et al [28], it can be shown that, when R 0 > 1, instability of E 0 implies uniform persistence of the model.…”

Section: Theorem 23: For Model 1mentioning

confidence: 95%

Understanding the effects of intermittent shedding on the transmission of infectious diseases: example of salmonellosis in pigs

Lahodny

Gautam

Ivanek

2017

Journal of Biological Dynamics

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A number of environmentally transmitted infectious diseases are characterized by intermittent infectiousness of infected hosts. However, it is unclear whether intermittent infectiousness must be explicitly accounted for in mathematical models for these diseases or if a simplified modelling approach is acceptable. To address this question we study the transmission of salmonellosis between penned pigs in a grower-finisher facility. The model considers indirect transmission, growth of free-living Salmonella within the environment, and environmental decontamination. The model is used to evaluate the role of intermittent fecal shedding by comparing the behaviour of the model with constant versus intermittent infectiousness. The basic reproduction number, R 0 , is used to determine the longterm behaviour of the model regarding persistence or extinction of infection. The short-term behaviour of the model, relevant to swine production, is considered by examining the prevalence of infection at slaughter. Comparison of the two modelling approaches indicates that neglecting the intermittent pattern of infectiousness can result in biased estimates for R 0 and infection prevalence at slaughter. Therefore, models for salmonellosis or similar infections should explicitly account for the mechanism of intermittent infectiousness. ARTICLE HISTORY

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Host–Pathogen Interactions

Smits¹,

Schokker²

2011

Systems Biology and Livestock Science

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Global dynamics of a SEIR model with varying total population size

Cited by 557 publications

References 23 publications

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Understanding the effects of intermittent shedding on the transmission of infectious diseases: example of salmonellosis in pigs

Host–Pathogen Interactions

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