“…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.…”
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.
“…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.…”
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.
“…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.…”
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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.