Estimation ofR₀from the initial phase of an outbreak of a vector-borne infection

Abstract

SummaryThe magnitude of the basic reproduction ratio R 0 of an epidemic can be estimated in several ways, namely, from the final size of the epidemic, from the average age at first infection, or from the initial growth phase of the outbreak. In this paper, we discuss this last method for estimating R 0 for vectorborne infections. Implicit in these models is the assumption that there is an exponential phase of the outbreaks, which implies that in all cases R 0 > 1. We demonstrate that an outbreak is possible, even in cases where R 0 is less than one, provided that the vector-to-human component of R 0 is greater than one and that a certain number of infected vectors are introduced into the affected population. This theory is applied to two real epidemiological dengue situations in the southeastern part of Brazil, one where R 0 is less than one, and other one where R 0 is greater than one. In both cases, the model mirrors the real situations with reasonable accuracy.keywords basic reproduction number, epidemiology, mathematical models, vector-borne infections, dengue fever

Analysis of the optimal vaccination age for dengue in Brazil with a tetravalent dengue vaccine

“…The remaining model parameters m = 1.5 (the number of vectors per host), τ = 7 days (the latency period in mosquitoes), b = 0.6 and c = 1 (the transmission probabilities from mosquitoes to humans A C C E P T E D M A N U S C R I P T and vice versa), which are needed to find the biting rate q from eq. (9) and hence λ, are taken from literature [37,45]. b, c and τ are assumed to be equal for all serotypes.…”

“…The parameter values µ M = 2.50 × 10 −2 day −1 , µ H = 3.72 × 10 −5 day −1 , and γ H = 0.14 day −1 were chosen from the literature [37,38]. λ can be found by fitting the number of new cases from an outbreak to an exponential curve for datasets of each serotype.…”

Modelling the dynamics of dengue real epidemics

“…There are many ways to estimate R 0 for vector-transmitted diseases using actual data of epidemics (Massad et al 2010). In this study, we estimated R 0 from the initial growth phase of the epidemics (Massad et al 2001).…”

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

“…It was when George Macdonald proposed his expression for what he defined as the "basic reproduction rate" (R 0 ) of malaria. In his words, it is defined as the number of secondary cases produced by a single infected individual (index case) along his/her infectious period in an entirely susceptible population (Macdonald 1952a, Dietz 1993, Massad et al 1994, 2010, Heesterbeek 2002, Lopez et al 2002, Burattini et al 2008. His derivation of R 0 is as follows.…”