Author: Alex Arenas; Wesley Cota; Jesus Gomez-Gardenes; Sergio Gomez; Clara Granell; Joan T. Matamalas; David Soriano-Panos; Benjamin Steinegger
Title: Derivation of the effective reproduction number R for COVID-19 in relation to mobility restrictions and confinement Document date: 2020_4_8
ID: nyjjaasw_137
Snippet: The model is amenable for analytical calculations. We calculate the basic reproduction number R 0 using the next generation matrix (NGM) approach [4] . Accordingly, we need to analyze the stability of the disease free equilibrium. We do so by making a first order expansion of the model equations for small values ( ) of the non-susceptible states m: ∼ Ï m,g i Ï S,h j ∀i, j, g, h and Ï m i 1 ∀i, where m ∈ {E, A, I, H, D, R}. The expansio.....
Document: The model is amenable for analytical calculations. We calculate the basic reproduction number R 0 using the next generation matrix (NGM) approach [4] . Accordingly, we need to analyze the stability of the disease free equilibrium. We do so by making a first order expansion of the model equations for small values ( ) of the non-susceptible states m: ∼ Ï m,g i Ï S,h j ∀i, j, g, h and Ï m i 1 ∀i, where m ∈ {E, A, I, H, D, R}. The expansion allows us to transform our discrete time Markov Chain into a system of continuous time differential equations. We start by expanding the infection probabilities P g i :
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