Topic
Next-generation matrix
About: Next-generation matrix is a research topic. Over the lifetime, 117 publications have been published within this topic receiving 6137 citations.
Papers published on a yearly basis
Papers
TL;DR: It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.
Abstract: The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.
5,010 citations
TL;DR: An elementary but complete proof that ℛ0 defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties.
Abstract: The basic reproduction number ℛ0 is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation...
2,022 citations
TL;DR: This primer article focuses on the basic reproduction number, ℛ0, for infectious diseases, and other reproduction numbers related to ℚ0 that are useful in guiding control strategies and theoretical ideas are applied to models that are formulated.
667 citations
TL;DR: The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus, and results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population.
Abstract: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number
$$R_0$$
. The model equations are solved numerically using fourth and fifth order Runge–Kutta methods. We found an
$$R_0$$
of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.
294 citations
TL;DR: In this article, the basic reproduction number for discrete-time epidemic models is calculated using the next generation matrix approach for discrete spatial patches and is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians.
Abstract: The next generation matrix approach for calculating the basic reproduction number is summarized for discrete-time epidemic models. This approach is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians. Two of the models include discrete spatial patches. For each model, is calculated in terms of the model parameters. For , if a small number of infectives is introduced, then the wildlife disease dies out. Global stability of the disease-free equilibrium is verified for a special case of the SI hantavirus model when . In addition, a numerical example indicates that there is a transcritical bifurcation at , with the disease dying out if but tending to an endemic level if .
225 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 18 |
| 2020 | 18 |
| 2019 | 17 |
| 2018 | 13 |
| 2017 | 12 |
| 2016 | 5 |