Estimating the reproductive number, total outbreak size, and reporting rates for Zika epidemics in South and Central America

Abstract

As South and Central American countries prepare for increased birth defects from Zika virus outbreaks and plan for mitigation strategies to minimize ongoing and future outbreaks, understanding important characteristics of Zika outbreaks and how they vary across regions is a challenging and important problem. We developed a mathematical model for the 2015/2016 Zika virus outbreak dynamics in Colombia, El Salvador, and Suriname. We fit the model to publicly available data provided by the Pan American Health Organization, using Approximate Bayesian Computation to estimate parameter distributions and provide uncertainty quantification. The model indicated that a country-level analysis was not appropriate for Colombia. We then estimated the basic reproduction number to range between 4 and 6 for El Salvador and Suriname with a median of 4.3 and 5.3, respectively. We estimated the reporting rate to be around 16% in El Salvador and 18% in Suriname with estimated total outbreak sizes of 73,395 and 21,647 people, respectively. The uncertainty in parameter estimates highlights a need for research and data collection that will better constrain parameter ranges.

Inferring the ecological drivers of arboviral outbreaks

“…These reporting rates were in stark contrast to estimated Zika reporting rates of 16% and 18% in El Salvador and Suriname, respectively (Shutt et al, 2017), but in agreement with observation rates of 2.7% in Cabo Verde Islands, West Africa (Lourenço et al, 2018). High seroprevalence levels of over 50% were also agreed with previous cross-sectional serological studies in Salvador, Brazil (Netto et al, 2017), Yap Island (Duffy et al, 2009), French…”

Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment

“…Similarly, the reporting rate parameters are now ${\kappa }_h^{*}={\kappa }_{h}N,{\kappa }_a^{*}={\kappa }_{a}C,$ and ${\kappa }_m^{*}={\kappa }_{m}C\pi ,$ so that the observed human cases or mosquito counts are the same as in the original model. However, we note that this means that the reporting rate and population-at-risk can now only be estimated as a combined parameter (as is common for infectious disease models both vector borne and otherwise (Shutt et al, 2017; Eisenberg et al, 2013; Evans et al, 2005)). Rescaling allows us to reduce the number of parameters explicitly included in the model and correct some of the immediately apparent identifiability issues.…”

“…There are numerous transmission models in mosquito-borne diseases, which frequently use parameter estimation in fitting these models to data, and broader issues of parameter uncertainty and sensitivity have often been raised and explored (Johnson et al, 2015; Manore et al, 2014; Prosper et al, 2012; Reich et al, 2013; Mendes Luz et al, 2003; Laneri et al, 2010; Pandey et al, 2013; Shutt et al, 2017). However, relatively few efforts have been made to formally examine questions of parameter identifiability in these models (Mendes Luz et al, 2003; Laneri et al, 2010; Bhadra et al, 2011; Moulay et al, 2012b; Pandey et al, 2013; Reiner et al, 2014; Zhu et al, 2015; Tuncer et al, 2016; Shutt et al, 2017).…”

“…However, relatively few efforts have been made to formally examine questions of parameter identifiability in these models (Mendes Luz et al, 2003; Laneri et al, 2010; Bhadra et al, 2011; Moulay et al, 2012b; Pandey et al, 2013; Reiner et al, 2014; Zhu et al, 2015; Tuncer et al, 2016; Shutt et al, 2017). Two studies that directly evaluated identifiability issues include: Denis-Vidal, Verdière, and colleagues assessed the structural (theoretical) identifiability of a chikungunya transmission model assuming all the states in human population and mosquito larva are observable (Moulay et al, 2012b; Zhu et al, 2015); Tuncer et al (2016) examined both structural and practical identifiability of a within-to-between host model of Rift Valley fever, addressing how the multi-scale nature of such immuno-epidemiological problems affects model identifiability.…”

Modeling Mayaro and Chikungunya Control Strategies in Rio de Janeiro Outbreaks

“…The model adopted here is a compartmental 36 model known as SEIR (Susceptible, Exposed, Infected, and Recovered) [8,10,14]. The 37 approaches using this class of models have been successful in modeling epidemic related 38 to human vector dynamics [11,15]. Fig 1 presents a schematic description of this 39 modeling.…”