The construction of next-generation matrices for compartmental epidemic models

By Odo Diekmann, J. Heesterbeek, M. Roberts. Journal of the Royal Society Interface, 2010

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Thermal biology of mosquito-borne disease (2019, methodology): “Reproduction numbers can be calculated using multiple methods, with differing interpretations (Heesterbeek 2002; Heffernan et al. 2005; Diekmann et al. 2009), although their direct application is limited in realistically variable environments (Baca€er & Guernaoui 2006; Baca€er & Ait Dads 2012).”
Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures (2020, methodology): “As the model is spatially explicit, we implement a generalized reproduction number, that is, the spectral radius of a next-generation matrix (NGM) (35, 36, 40, 41), that measures the potential spread in the absence of containment interventions ( Materials and Methods ).”
Mathematical perspective of Covid-19 pandemic: Disease extinction criteria in deterministic and stochastic models (2020, positive): “We determine the basic reproduction number (BRN), R 0 , associated with the deterministic system (1) using the “next generation matrix” approach [38, 39].”