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R0: The maths behind the Basic Reproduction Number
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Explains the important concept of Basic Reproduction Number (R0, R-nought), provides mathematical justification for the definition of R0 as the Dominant Eigenvalue of the Next Generation Matrix, and shows how it generalises across a range of different disease transmission structures. Also provides examples of the Next Generation Matrix, and the associated R0 (dominant eigenvalue) for Vector-Host disease (malaria), SIR model, and multi-group SEIR model. For references and further readings, please see below:
1) Diekmann, Heesterbeek, and Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990).
2) Diekmann, Heesterbeek, and Roberts. The construction of next-generation matrices for compartmental epidemic models. The Royal Society (2009)
3) Heesterbeek. A Brief History of R0 and a Recipe for its Calculation. Acta Biotheor 50, 189–204 (2002).
1) Diekmann, Heesterbeek, and Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990).
2) Diekmann, Heesterbeek, and Roberts. The construction of next-generation matrices for compartmental epidemic models. The Royal Society (2009)
3) Heesterbeek. A Brief History of R0 and a Recipe for its Calculation. Acta Biotheor 50, 189–204 (2002).
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R0: The maths behind the Basic Reproduction Number
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