Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

Webb, Glenn; Hsieh, Y-H.; Wu, Jianhong

doi:10.1051/mmnp/20105312

Cited by 14 publications

(10 citation statements)

References 41 publications

(45 reference statements)

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“…Furthermor e, viral shedding during the preclinical stage of infection was confirmed to occur in approximately 1-8% of infections [22] and preclinical transmis sion was also recorded in early H1N1 outbreaks [23]. Mathema tical models have demonstrated how preclinical transmission can influence the magnitude of outbreaks in large closed populations , such as schools, workplaces and military facilities, and highlight s the importance of such transmis sion in the decision process [24]. In particular, a greater transmis sion ability during the preclinic al period has been associated with children [25] and this increases the need to understa nd the effects of this state on the disease pathway.…”

Section: An Alternative Modelling Approachmentioning

confidence: 99%

“…The system (14)- (20) always has a disease-fr ee equilibrium P 0 . An endemic equilibrium b P, given by (21)- (24) and where only the drug-resista nt strain is present in the population, exists when R 2 > 1. Another endemic equilibrium P Ã , given by (25)-(31) and where both drug-sens itive and drug-resistant strains are present, exists when R 1 > 1 and R 1 > R 2 .…”

Section: Basic Reproduction Number and Equilibriamentioning

confidence: 99%

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A model for the emergence of drug resistance in the presence of asymptomatic infections

Robinson

Stilianakis

2013

Mathematical Biosciences

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An analysis of a mathematical model, which describes the dynamics of an aerially transmitted disease, and the effects of the emergence of drug resistance after the introduction of treatment as an intervention strategy is presented. Under explicit consideration of asymptomatic and symptomatic infective individuals for the basic model without intervention the analysis shows that the dynamics of the epidemic is determined by a basic reproduction number R0. A disease-free and an endemic equilibrium exist and are locally asymptotically stable when R0<1 and R0>1 respectively. When treatment is included the system has a basic reproduction number, which is the largest of the two reproduction numbers that characterise the drug-sensitive (R1) or resistant (R2) strains of the infectious agent. The system has a disease-free equilibrium, which is stable when both R1 and R2 are less than unity. Two endemic equilibria also exist and are associated with treatment and the development of drug resistance. An endemic equilibrium where only the drug-resistant strain persists exists and is stable when R2>1 and R11 and R1>R2 and both drug-sensitive and drug-resistant strains are present. The analysis of the system provides insights about the conditions under which the infection will persist and whether sensitive and resistant strains will coexist or not.

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Section: An Alternative Modelling Approachmentioning

confidence: 99%

Section: Basic Reproduction Number and Equilibriamentioning

confidence: 99%

A model for the emergence of drug resistance in the presence of asymptomatic infections

Robinson

Stilianakis

2013

Mathematical Biosciences

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“…3b, which corresponds to a scenario when one or several public places encounter a series of smallpox virus releases. T v = 3 days [30] length of infectious period F i = 28 days [30] infection transmission rate function removal of symptomatic cases R sym ≥ 50% per day [26,35] isolation rate of infectives µ (a) = 0.0,…”

Section: Model Parametersmentioning

confidence: 99%

“…After the outbreak of SARS in 2003, ordinary differential equations models were used in many SARS literatures [2,7,9,10,11,12,14,16,17,19,28,33]. Partial differential equation models with infection-age were developed in [12], [20], and [35]. But as pointed out in [3], most of the previous studies modeled linear contact tracing processes.…”

mentioning

confidence: 99%

Modeling of contact tracing in epidemic populations structured by disease age

2015

DCDS-B

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We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-agedependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1) we assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack; (2) we simulate the 2003 SARS outbreak in Taiwan and estimate the number of cases avoided by contact tracing. Our model can be applied as a rational basis for decision makers to guide interventions and deploy public health resources in future epidemics.2010 Mathematics Subject Classification. Primary: 92D30; Secondary: 35Q92.

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“…These interventions have economic costs to individuals and society related to lost work, increased school absenteeism and decreased business revenues [1,2,3,4,5].…”

Section: Introductionmentioning

confidence: 99%

Modelling influenza A(H1N1) 2009 epidemics using a random network in a distributed computing environment

et al. 2015

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In this paper we propose the use of a random network model for simulating and understanding the epidemics of influenza A(H1N1). The proposed model is used to simulate the transmission process of influenza A(H1N1) in a community region of Venezuela using distributed computing in order to accomplish many realizations of the underlying random process. These large scale epidemic simulations have recently become an important application of high-performance computing. The network model proposed performs better than the traditional epidemic model based on ordinary differential equations since it adjusts better to the irregularity of the real world data. In addition, the network model allows the consideration of many possibilities regarding the spread of influenza at the population level. The results presented here show how well the SEIR model fits the data for the AH1N1 time series despite the irregularity of the data and returns parameter values that are in good agreement with the medical data regarding AH1N1 influenza virus. This versatile network model approach may be applied to the simulation of the transmission dynamics of several epidemics in human networks. In addition, the simulation can provide useful information for the understanding, prediction and control of the transmission of influenza A(H1N1) epidemics.

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Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

Cited by 14 publications

References 41 publications

A model for the emergence of drug resistance in the presence of asymptomatic infections

A model for the emergence of drug resistance in the presence of asymptomatic infections

Modeling of contact tracing in epidemic populations structured by disease age

Modelling influenza A(H1N1) 2009 epidemics using a random network in a distributed computing environment

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