Perspectives on the basic reproductive ratio

Heffernan, Jane M.; Smith, Robert J.; Wahl, Lindi M.

doi:10.1098/rsif.2005.0042

Cited by 1,043 publications

(902 citation statements)

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“…However, there are alternative methods such as the graph theoretic method (de Camino-Beck, Lewis, & van den Driessche, 2009). While we do not discuss them in this paper, a nice discussion can be found in Heffernan, Smith, and Wahl (2005) and Li, Blakeley, and Smith (2011).…”

Section: Other Methods For Finding Rmentioning

confidence: 99%

An introduction to compartmental modeling for the budding infectious disease modeler

Blackwood

Childs

2018

Letters in Biomathematics

112

146

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Section: Other Methods For Finding Rmentioning

confidence: 99%

An introduction to compartmental modeling for the budding infectious disease modeler

Blackwood

Childs

2018

Letters in Biomathematics

112

146

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“…At each time point, we use the nextgeneration method [37] to calculate the effective reproductive rate R E to measure the transient risk. Essentially, at each time point, we compute the matrix F as a proportion of new infections from each age group and also matrix V as the proportion of individuals transferring out due to recovery, ageing and death from respective compartments.…”

Section: Methodsmentioning

confidence: 99%

Age-specific mixing generates transient outbreak risk following critical-level vaccination

Bhattacharyya

Ferrari

2016

Epidemiol. Infect.

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SUMMARYMeasles elimination goals have been adopted in a range of countries, sub-regions, and regions since the WHO declared an elimination goal by 2015 or 2020. All countries attempt to achieve and maintain high coverage through routine immunization programmes. This routine strategy, however, does not ensure the elimination goal of measles. Many developed countries, such as the United States, that have succeeded in interrupting measles transmission earlier, are now experiencing outbreaks with an increasing number of cases. Using a stochastic, age-structured model of measles vaccination dynamics, we explore and characterize the transient dynamics of measles susceptibility in the years following the implementation of routine vaccination at the herd immunity threshold. We demonstrate how a population could face risks of potentially large outbreaks even within few years of vaccination. We characterize different risk profiles depending on the incidence pattern in the years prior to vaccination. These results suggest that the classic critical vaccination threshold is necessary to achieve herd immunity, but not sufficient to prevent long periods of transient, super-critical dynamics. Our results suggest the need of future work for more careful monitoring of the impacts of current immunization programmes, and developing models that take into account more complicated vaccination strategies, demographic factors, and population movements.

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“…Other methods calculate R 0 via the positivity condition of the infected steady-state density [42,43]. In this case R 0 is simply the inverse of the proportion of the remaining susceptibles [44].…”

Section: Basic Reproduction Numbers and Epidemiological Feedbackmentioning

confidence: 99%

From within-host interactions to epidemiological competition: a general model for multiple infections

Sofonea

Alizon

Michalakis

2015

Phil. Trans. R. Soc. B

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One contribution of 17 to a theme issue 'Within-host dynamics of infection: from ecological insights to evolutionary predictions'. Many hosts are infected by several parasite genotypes at a time. In these coinfected hosts, parasites can interact in various ways thus creating diverse within-host dynamics, making it difficult to predict the expression and the evolution of virulence. Moreover, multiple infections generate a combinatorial diversity of cotransmission routes at the host population level, which complicates the epidemiology and may lead to non-trivial outcomes. We introduce a new model for multiple infections, which allows any number of parasite genotypes to infect hosts and potentially coexist in the population. In our model, parasites affect one another's within-host growth through density-dependent interactions and by means of public goods and spite. These within-host interactions determine virulence, recovery and transmission rates, which are then integrated in a transmission network. We use analytical solutions and numerical simulations to investigate epidemiological feedbacks in host populations infected by several parasite genotypes. Finally, we discuss general perspectives on multiple infections.

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Perspectives on the basic reproductive ratio

Cited by 1,043 publications

References 72 publications

An introduction to compartmental modeling for the budding infectious disease modeler

An introduction to compartmental modeling for the budding infectious disease modeler

Age-specific mixing generates transient outbreak risk following critical-level vaccination

From within-host interactions to epidemiological competition: a general model for multiple infections

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