What is the reproductive number of yellow fever?
Ying Liu
Joacim Rocklöv
To whom correspondence should be addressed. Tel.: +46706361635; Email:joacim.rocklov@umu.se
Received 2020 Aug 28; Accepted 2020 Aug 31; Revision requested 2020 Aug 31; Collection date 2020 Oct.
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Abstract
Teaser Our review found the average reproductive numberR0 for yellow fever to be 4.81 with a median of 4.21.
Keywords: Basic reproductive number, yellow fever vaccine, critical vaccine level, flavivirus, epidemic potential, Latin America, traveller
Yellow fever is a viral vector-borne disease caused by the yellow fever virus with its geographic distribution currently limited to sub-Saharan Africa and South America. The case fatality rate of hospitalized severe yellow fever is above 40%.1
The basic reproductive number,R0, can be used to characterize the epidemic potential of a pathogen by assessing the number of secondary cases that would be generated by one infectious case if it was to be introduced into an immunologically naïve population.R0 values that are larger than 1 indicate epidemic growth; values around 1 represent endemicity and for values below 1, the outbreak is declining and the number of new infections will be decreasing in subsequent generations. We conducted a review of published peer-reviewed literature on the estimates of the basic reproductive number of yellow fever and discuss the implications for herd immunity in relation to the critical vaccination levels.
We conducted searches on PubMed and Web of Science with the following search terms ‘yellow fever AND (R0 OR basic reproductive number)’. The restriction on published article language was English. We included all publications from 1950 until August 2020. Our review excluded the estimates of the effective reproductive number that depends on the background level of immunity.
A total of 31 studies were identified through the literature search based on these search terms. We excluded 23 studies because of ineligible or incomplete outcome data. Eight studies were included in the final analysis. Overall, 11 data points were collated from the included studies.R0 estimates were derived for a variety of countries, study years and methods as provided inTable 1. The estimates range from 1.35 to 11. The averageR0 was 4.81 with a median of 4.21 and an interquartile range of 2.19.
Table 1.
Published estimates ofR0 for yellow fever
| Study | Location | Study year | R0 estimates | Method |
|---|---|---|---|---|
| Zhaoet al.2 | Luanda, Angola | 2015–2016 | 6(range 4–8) | Estimated from mathematical compartmental based model |
| Kraemeret al.3 | Angola | 2015–2016 | 4.8 (95% CI: 4.0–5.6) | Formula linking to the exponential growth rate and the generation time distribution |
| Wuet al.4 | Angola | 2016 | 5.2 (95% CI: 4.3–6.1) | Wallinga and Teunis method, assuming mean mosquito lifespan = 7 days |
| Wuet al.4 | Angola | 2016 | 7·1 (95% CI 5.5–8.7) | Wallinga and Teunis method, assuming mean mosquito lifespan = 14 days |
| Kennedyet al.5 | Memphis, Tennessee, USA | 1878 | 11 | Estimated from mathematical compartmental-based model |
| Johanssonet al.6 | Asuncio’n, Paraguay | 2008 | 4.1 | Using moderate literature estimates of the parameters for the human infectious period,R0 = average number of infectious mosquitoes produced per infectious human * the average number of infectious humans produced per infectious mosquito |
| Curtiset al.7 | New Orleans, USA | 1878 | 2.38 | R0 was calculated at the neighbourhood level applying a mathematical equation; Constrained |
| Curtiset al.7 | New Orleans, USA | 1878 | 3.59 | R0 was calculated at the neighbourhood level applying a mathematical equation; Unconstrained |
| Massadet al.8 | Sao Paulo State, Brazil | 2001 | 3.23 (range 1.62–6.61) | CalculateR0 for yellow fever for every city thatR0 of dengue>1, using a mathematical function ofR0 for dengue with dengue cases |
| Massadet al.9 | Sao Paulo State, Brazil | 2000 | 4.21(range 2.39–8.59) | EstimateR0 of yellow fever using a mathematical function ofR0 for dengue with the annual outbreaks of dengue in 2000 |
| Massadet al.9 | Sao Paulo State, Brazil | 1991 | 1.35(range 1.07–1.66) | EstimateR0 of yellow fever using a mathematical function ofR0 for dengue with the annual outbreaks of dengue in 1991 |
TheR0 estimates appear to vary between studies. Partly, this can be related to methodological differences, but also different local susceptibility and exposure to vectors, i.e. which could be emphasized during due El Nino period and in warmer climate. A relationship betweenR0 and climate has been observed for other viruses transmitted by the same vector (Liuet al., 2020 in Supplementary data).
TheR0 is an important number for elimination and it should be considered at a high average/aggregation level over time and space as it is the long-term elimination that is being considered.
With increasing global travel patterns (at least before the COVID-19 pandemic), the risk of importation of yellow fever to vulnerable countries where the vector is present but no adequate vaccination coverage exists is high.10 The critical vaccination level corresponds to the proportion of population that need to be vaccinated to achieve herd immunity assuming the population is vaccinated at random and that the population is mixing homogenously. Therefore, in the hypothetical situation when a vaccine is 100% effective (i.e.E = 1), the critical vaccination level equals the herd immunity level,Vc = 
; otherwise it isVc = 
. Assuming a vaccine efficacy of 99% [30 days after vaccination (WHO, 2019 in Supplementary data)], we calculated that the critical vaccine coverage levels need to be between 26.2, 77.0 and 91.8% according to the minimum, median and maximumR0 values, respectively. Reaching very highVc levels, such as 91.8%, for herd immunity is logistically not feasible in many current settings.
We conclude that vaccine coverage thresholds may vary between areas and countries as the basic reproductive number can vary substantially in different localities.
Supplementary data
Supplementary data are available atJTM online.
Funding
Svenska Forskningsrådet Formas (Swedish Research Council Formas) (Grant Number: 2018–01754).
Conflict of interest
None declared.
Author contributions
J.R. had the idea, and Y.L. did the literature search and created the table. Y.L. wrote the first draft; Y.L. and J.R. drafted the final manuscript. All authors contributed to the final manuscript.
Supplementary Material
Contributor Information
Ying Liu, School of International Business, Xiamen University Tan Kah Kee College, Zhangzhou 363105, China.
Joacim Rocklöv, Department of Public Health and Clinical Medicine, Section of Sustainable Health, Umeå University, Umeå, Sweden; Heidelberg Institute of Global Health, University of Heidelberg, Heidelberg, Germany.
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