Abstracts
OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengueinfested area. METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in São Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS: Currently there is a great number of nonvaccinated people living in Aedes aegypti infested area in the state of São Paulo.
Yellow fever; Dengue; Mathematical models; Disease outbreaks; Aedes; Yellow fever vaccine
OBJETIVO: Propor um modelo matemático para a estimativa da reprodutibilidade basal, R0, para a febre amarela urbana em uma área infestada pela dengue. MÉTODOS: O método utilizado considera que, como ambas as doenças são transmitidas pelo mesmo vetor (Aedes aegypti), poderseia aplicar todos os parâmetros quantitativos relativos ao mosquito, estimados pela fase inicial da curva de crescimento de casos de dengue, à dinâmica da febre amarela. Demonstrase que o R0 da febre amarela é em média 43% menor que o da dengue. Esta diferença devese à viremia mais prolongada da dengue, bem como ao menor período de incubação extrínseco daquele vírus no mosquito. RESULTADOS: Apresentase a aplicação desta análise matemática à situação epidemiológica da dengue no estado de São Paulo, para o ano de 2001, onde o número de casos de dengue aumentou de 3.582, em 2000 para 51.348, em 2001. Calculouse o valor de R0 para a febre amarela para cada cidade do estado que tinha R0 para dengue maior que um. Estimouse o número total de pessoas desprotegidas, sem vacina, e que vivem em áreas de alto risco para a febre amarela urbana. CONCLUSÕES: Foi demonstrado que existe, um grande contingente de pessoas não vacinadas contra febre amarela vivendo em áreas infestadas por Aedes aegypti no Estado de São Paulo, até aquela data (2001).
Febre amarela; Dengue; Modelos matemáticos; Surtos de doenças; Aedes; Vacina contra febre amarela
ORIGINAL ARTICLES
Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil
Dengue e risco da reintrodução da febre amarela urbana no Estado de São Paulo
Eduardo Massad; Marcelo Nascimento Burattini; Francisco Antonio Bezerra Coutinho; Luiz Fernandes Lopez
Faculdade de Medicina da Universidade de São Paulo. São Paulo, SP, Brasil
^{Correspondence} Correspondence to Eduardo Massad Faculdade de Medicina  USP Av. Dr. Arnaldo, 455 CEP: 01246903. São Paulo, SP, Brasil Email: edmassad@usp.br
ABSTRACT
OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R_{0}, of urban yellow fever in a dengueinfested area.
METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R_{0} for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period.
RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in São Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R_{0} for yellow fever for every city which have shown R_{0} of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever.
CONCLUSIONS: Currently there is a great number of nonvaccinated people living in Aedesaegypti infested area in the state of São Paulo.
Keywords: Yellow fever, epidemiology. Dengue, epidemiology. Mathematical models. Disease outbreaks. Aedes. Yellow fever vaccine.
RESUMO
OBJETIVO: Propor um modelo matemático para a estimativa da reprodutibilidade basal, R_{0}, para a febre amarela urbana em uma área infestada pela dengue.
MÉTODOS: O método utilizado considera que, como ambas as doenças são transmitidas pelo mesmo vetor (Aedes aegypti), poderseia aplicar todos os parâmetros quantitativos relativos ao mosquito, estimados pela fase inicial da curva de crescimento de casos de dengue, à dinâmica da febre amarela. Demonstrase que o R_{0} da febre amarela é em média 43% menor que o da dengue. Esta diferença devese à viremia mais prolongada da dengue, bem como ao menor período de incubação extrínseco daquele vírus no mosquito.
RESULTADOS: Apresentase a aplicação desta análise matemática à situação epidemiológica da dengue no estado de São Paulo, para o ano de 2001, onde o número de casos de dengue aumentou de 3.582, em 2000 para 51.348, em 2001. Calculouse o valor de R_{0} para a febre amarela para cada cidade do estado que tinha R0 para dengue maior que um. Estimouse o número total de pessoas desprotegidas, sem vacina, e que vivem em áreas de alto risco para a febre amarela urbana.
CONCLUSÕES: Foi demonstrado que existe, um grande contingente de pessoas não vacinadas contra febre amarela vivendo em áreas infestadas por Aedes aegypti no Estado de São Paulo, até aquela data (2001).
Descritores: Febre amarela, epidemiologia. Dengue, epidemiologia. Modelos matemáticos. Surtos de doenças. Aedes. Vacina contra febre amarela.
INTRODUCTION
In a recent publication (Massad et al,^{11} 2001) it was proposed a mathematical method for the estimation of the Basic Reproduction Number, R_{0} (Anderson & May,^{1} 1991), and hence the threshold for triggering a major epidemic of urban yellow fever in a dengueinfested area. The method is based on the assumption that, as the vector of both infections is the Aedes aegypti, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic (see below), could be applied to yellow fever dynamics. It was demonstrated that R_{0} for yellow fever is, on average, 34% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period (Monath,^{12} 1990; Halsted,^{8} 1990). It was then exemplified the method with dengue epidemic data from the state of São Paulo, Brazil, for the year 2000. At that time, 67 cities (about 10% of the total number of cities in the state) presented dengue cases with 12 of them showing R_{0}>1 for both dengue and yellow fever. As the measures for vector control were inadequate, the dengue epidemic spread throughout the state of São Paulo in the following year (2001), becoming worse in intensity and number of cities affected, and therefore increasing the risk of urban yellow fever being reintroduced.
Early in the 20th century, when it was discovered that the yellow fever virus is transmitted in its urban cycle by Aedes aegypti, control measures were introduced leading to its almost disappearance of the Americas and, in particular, of Brazil. However, reinfestation with Aedes aegypti vector, which began in the late 1960s (Fraiha,^{6} 1968; Franco,^{7} 1969; Monath,^{13} 1999), is now practically complete, and vector control is substantially more difficult than before.
Dengue, another Flaviridae infection transmitted by the same peridomestic Aedes aegypti mosquitoes, reappeared as a major urban epidemic in Brazil in the state of Rio de Janeiro in 1986, although there has been a previous outbreak of dengue virus reported in Brazil (Marques et al,^{10} 1994; Degallier et al,^{3} 1996). Since then, it turned into an endemic infection with annual outbreaks, comprising more than 80,000 cases reported in the state of São Paulo in the last 5 years, of which approximately 52,000 cases occurred in 2001.
There has been no case of urban yellow fever reported in Brazil since 1942 (CVE^{1} 1 Center for Epidemiologic Surveillance. Data available in 2001. Http://www.cve.sp.gov.br/htm/febre_am1.htm 2001). The sylvatic yellow fever, however, is enzootic in an enormous area of central and northnorthwestern states. In the period between 1990 and 2001, 380 human cases (with 159 deaths) were reported, of which 191 (82 deaths) were reported in the last three years (CVE 2001). In addition, the epidemic is drifting from its original epicenter in the northern and central regions towards the more populated southeastern states. In 2000, two autochthonous human cases were reported in the state of São Paulo, the first ones in more than 50 years.
It should be mentioned that although Aedes albopictus is also present in costal areas of Brazil since the early 1980s (Forattini,^{4} 1986), it was not included in the study analysis because its role as an important dengue transmitter in the Americas is still to be confirmed (Forattini,^{5} 2002).
In this study the analysis presented in Massad et al,^{11} 2001, is expanded and data from the 2001 dengue epidemic updated. In addition it is estimated the number of cities with major risk of urban yellow fever reintroduction and the size of the population at risk.
In the next section it is briefly described the method proposed in Massad et al,^{11} 2001, for the estimation of R_{0} for yellow fever as a function of R_{0} for dengue, estimated from the exponential growing phase of the dengue epidemic. Section 3 is dedicated to the description and analysis of the dengue epidemic in the state of São Paulo in 2001 and its potential repercussion on the risk of urban yellow fever reintroduction in affected areas. It is also estimate the total number of unprotected people living in highly risky areas for exposure to urban yellow fever. Finally, in the discussion section there are some observations on the current (2002) dengue epidemic in São Paulo and possible control strategies for avoiding a major epidemic of urban yellow fever in the dengue infested area are assessed.
Estimating R_{0} for yellow fever
For a vectorborne disease, R_{0} may be understood as the number of secondary infections spread in a community through the vector population, as direct result of the presence of a single primary case (Macdonald,^{9} 1952; Molineaux & Gramiccia,^{15} 1980; Burattini et al,^{2} 1998).
The expression for R_{0} is given by (Massad et al,^{11} 2001; Burattini et al,^{2} 1998):
where N_{H} is the total number of humans and N_{M} is the total number of mosquitoes. Each female mosquito bites humans at a rate of a times per unit of time. The duration of viremia (and therefore infectiousness) of a given vectorborne infection is g^{1} units of time. Only a fraction of bites in infected humans, c, is considered to be infective to the vectors. The average life expectancy of the mosquitoes is µ^{1} and t is the extrinsic incubation period of the infection. After t units of time, only a fraction e^{µt} of mosquitoes survive and only a proportion b of their bites is effectively infective to humans.
From equation (1) it can be deduced a relation between R_{0} of yellow fever and dengue. The resulting expression of R_{0} for yellow fever as a function of R_{0} for dengue is given by (Massad et al,^{11} 2001):
It is also demonstrated in that previous study that R_{0} for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer viremia of dengue and its shorter extrinsic incubation period (Massad et al,^{11} 2001).
The relation between the critical proportion of any control measure to be applied to a population in order to ensure the nonexistence of a disease and the value of its R_{0} is given by (Anderson & May,^{1} 1991):
Therefore, if a proportion p of the susceptible population is vaccinated (and considered protected), then the critical proportion, p_{c}, to vaccinate against yellow fever in order to ensure that a single infective would not trigger an epidemic is (Massad et al,^{11} 2001):
Estimating R_{0} from the initial exponential phase of the number of cases
As mentioned in Massad et al,^{11} 2001, in an epidemic of a vectorborne infection, R_{0} can be estimated from the initial exponential growing phase of the number of cases in each affected city, i.
Fitting a exponential
C_{Hi} is a constant to the initial growing phase of the dengue number of human cases I_{Hs}, and it can be estimated the coefficient l, from which R_{0}_{dengue} can be calculated for each affected city i, according to:
Having R_{0}_{dengue} it is possible to estimate R_{0}_{yf} and p_{c} from equations (2) and (3), respectively.
The dengue epidemic in São Paulo in 2001
Dengue reemerged in Brazil in 1986 and since then it has recurred with varying intensity every year. In São Paulo, after the first minor epidemics in the late 1980's, dengue has acquired alarming proportions with yearly epidemics of growing intensity and range of geographical spread.
As mentioned before, the number of affected cities in 2000 (67), 12 showing R_{0} greater than one, increased to 191, of which 64 with R_{0}>1. The total number of dengue cases in the state of São Paulo increased from 3,582 in the year 2000 to 51,348 in the year 2001. In the current year, 3,945 cases were confirmed in the state of São Paulo in the first 9 weeks of the year. Table 1 shows the temporal evolution of dengue cases in the state of São Paulo since 1987.
In Table 2 the dengue situation is described for the 64 cities with R_{0}>1 for dengue in the year 2001. The first column shows the name of the city; the second shows the total number of reported cases in those cites; the third column shows the estimated value of R_{0} _{dengue}; the fourth column shows the calculated values of R_{0y}_{ƒ}; and the last column shows the estimated proportion of individuals that should be vaccinated against yellow fever in order to prevent an epidemic.
In Figures 1a and 1b, the epidemic evolution is presented for 2000 and 2001. The figures show a map of São Paulo, where light gray areas are those municipalities infested by Ae. aegypti but with no cases of dengue reported; dark gray areas are the municipalities with dengue cases reported; and black areas are those municipalities with dengue epidemic and R_{0}>1.
In Table 3 present the same cities mentioned above with their respective population sizes, actual proportion of individuals vaccinated against yellow fever in the last 10 years, and number of individuals at risk (unprotected by vaccination).
Figure 2a shows the current control strategy against yellow fever in the state of São Paulo. Shaded areas represent municipalities included in what is called a "transition zone," between enzootic and unscathed regions of Brazil, thought to be at risk for yellow fever. Therefore, these are the cities under intense surveillance and where vaccination is recommended, creating a blocking belt.
In contrast, Figure 2b show what it is believed to be a better representation of the actual risk of urban yellow fever reintroduction in São Paulo. The figure shows the same light gray areas (as in Figure 1) infested with Ae. aegypti, dark gray areas representing the blocking belt as in Figure 2a, and those cities with R_{0} for yellow fever greater than 1, i.e., at risk of urban yellow fever reintroduction. Yellow areas indicate municipalities with vaccination against yellow fever below the critical proportion required to prevent an epidemic that could be triggered by a single imported case from the sylvatic yellow fever endemic areas. Green areas represent those municipalities with R_{0} for yellow fever greater than 1 but with vaccination above that critical proportion.
DISCUSSION
Since the last three cases of urban yellow fever reported in Brazil in 1942, the disease has been confined to enzootics of the sylvatic form (FUNASA,^{2} 2 " Fundação Nacional de Saúde, Ministério da Saúde, Brasil". Data available in 2001. Http://www.funasa.gov.br 2001). This is perpetuated by a cycle involving primates and mosquitoes of the gender Haemagogus sp. and Sabethes sp. Sporadic human cases of the sylvatic form have been reported since then, with a total of 380 (159 deaths) cases between 1990 and 2001. This relatively low number of cases is due to basically two factors: low migration rates between urban centers and enzootic reservoirs and an effective vaccination program encouraging people to be vaccinated 10 days before visiting enzootic areas. In addition, this control program includes an intense surveillance program of Ae. aegypti and vaccination creating a blocking belt of vaccinated individuals living in the transition zone between urbanized areas and enzootic regions.
The state of São Paulo shares borders with enzootic states. In spite of that only two autochthonous cases of sylvatic yellow fever has been reported so far. However, the spread of Aedes aegypti towards coastal areas, and the ensuing spread of dengue, is putting at risk cities far away from the blocking belt vaccination areas, as shown in Figure 2b. A global vaccination campaign against yellow fever should be carried out with great care. Although safe the vaccine is not free from adverse effects (Monath,^{14} 1999). In Brazil, it has been estimated between 1 and 21 fatality cases per million doses (Struchiner, personal communication). At the moment, considering the worsening of dengue epidemic in São Paulo (more than 10,000 cases reported in the first 8 weeks of the year), and considering the adverse effects of the yellow fever vaccine, the current vaccination strategy should be revised.
The current preventive program of vaccination focuses on areas of the state as shown in Figure 2a, part of the blocking belt. In addition, vaccination of people traveling to enzootic regions is strongly recommended. However, as shown in Figure 2b, this strategy is inconsistent with the current epidemiological scenario of the state of São Paulo. It is worth noting that only 16% of the municipalities in the blocking belt have R_{0} for yellow fever greater than 1. Furthermore, only 26% of the cities with R_{0} for yellow fever greater than 1 have achieved protective coverage levels. Therefore, it could be that the state of São Paulo is wasting vaccines and resources, and posing a risk of adverse effects to people by routinely vaccinating the remaining 84% of the cities in the blocking area which have R_{0} for yellow fever lower than 1 while failing to protect those cities at actual risk.
More serious is the fact that half of the 61 cities with R_{0} for yellow fever greater than 1 and inadequate vaccination are outside the blocking belt area, and none of them have achieved the minimum vaccination coverage required.
Therefore vaccination strategy should be urgently revised, as follows: 1) it is important to take into account regional variation in the risk of yellow fever using the new methodology proposed in (1) and applied here for the identification of areas at risk and then periodical calculation of that risk should be undertaken; 2) a compulsory vaccination program for people traveling to enzootic areas should be introduced and the education program to warn people of the risk of traveling to those areas without vaccination at least 10 days prior should be improved; 3) routine vaccination should be targeted to the areas at risk in order to avoid unnecessary mass vaccination. This proposed targeted vaccination program would be also more cost effective in the sense that it optimizes allocation of limited resources.
Currently there are more than 15 million nonvaccinated people living in Aedes sp. infested area in the state of São Paulo. Although the dramatic dengue epidemic is attracting the attention of public health authorities, these figures are of high concern. The risk of reemergence of urban yellow fever is indeed on one's doorstep.
Supported by grants of LIM01/HCFMUSP, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP  Processo n. 2000/013474), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq  Processo n. 304560/901) and PRONEX. (Processo n. 41.96.0937)
Received on 12/9/2002
Reviewed on 17/3/2003
Approved on 7/4/2003
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Publication Dates

Publication in this collection
29 Mar 2004 
Date of issue
Aug 2003
History

Received
12 Sept 2002 
Reviewed
17 Mar 2003 
Accepted
07 Apr 2003