Effects of migration rates and vaccination on the spread of yellow fever in Latin American communities.

Objective: To assess how relevant the flow of people between communities is, compared to vaccination and type of vector, on the spread and potential outbreaks of yellow fever in a disease-free host community. Methods: Using a SEIRV-SEI model for humans and vectors, we applied numerical simulations to the scenarios: (1) migration from an endemic community to a disease-free host community, comparing the performance of Haemagogus janthinomys and Aedes aegypti as vectors; (2) migration through a transit community located on a migratory route, where the disease is endemic, to a disease-free one; and (3) effects of different vaccination rates in the host community, considering the vaccination of migrants upon arrival. Results: Results show no remarkable differences between scenarios 1 and 2. The type of vector and vaccination coverage in the host community are more relevant for the occurrence of outbreaks than migration rates, with H. janthinomys being more effective than A. aegypti. Conclusions: With vaccination being more determinant for a potential outbreak than migration rates, vaccinating migrants on arrival may be one of the most effective measures against yellow fever. Furthermore, H. janthinomys is a more competent vector than A. aegypti at similar densities, but the presence of A. aegypti is a warning to maintain vaccination above recommended levels.

Differences in Placental Histology Between Zika Virus-infected Teenagers and Older Women.

In pregnant women, Zika virus (ZIKV) is associated with a congenital syndrome, most frequently involving damage to embryo brain formation and the development of microcephaly. The mechanism(s) by which ZIKV enters the maternal-fetal interface and is transmitted to the fetus remains incompletely determined. We sought to evaluate histologic changes in the placenta of ZIKV-infected pregnant women and to determine if this varied by maternal age. Placental samples were obtained from 66 women, 33 of whom were positive for ZIKV. Histologic evaluations were performed on 4 areas of the placenta: fetal surface, maternal surface, umbilical cord, and membranes. Samples were analyzed by the tissue microarray technique and tested for CD4, CD8, CD20, CD68, FOXP3, and cyclooxygenase-2 expression. Data were evaluated using Fisher exact test. ZIKV infection was more frequent in women less than 18 yr of age (9/11, 81.8%) than in women above 18 yr old (24/55, 43.6%) (P=0.0440). ZIKV detection was associated with neutrophilic chorioamnionitis (P=0.0332) and with septal (P=0.0244) and villous (P=0.0534) calcification. Hofbauer cell hyperplasia (P=0.0260) and cyclooxygenase-2 expression (P=0.0346) were more prevalent in ZIKV-positive women aged 18 yr and below than in the older ZIKV-positive women. ZIKV infection during pregnancy occurs more frequently in adolescents and induces higher rates of damage at the maternal-fetal interface than in older women.

On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil.

BACKGROUND: During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate such side effects, many countries have implemented socioeconomic programs to fund individuals that lost their jobs and to help endangered businesses to survive. METHODS: We assess the role of a socioeconomic program, so-called "Auxilio Emergencial" (AE), during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. Then, we analyse the correlations between the reproduction number, the amount of individuals receiving governmental aid, and the index of social isolation based on mobile phone information. RESULTS: We observed significant positive correlation values between the average values by the AE and median values of an index accounting for individual mobility. We also observed significantly negative correlation values between the reproduction number and this index on individual mobility. Using the simulations of a susceptible-exposed-infected-removed-like model, if the AE was not operational during the first wave of COVID-19 infections, the accumulated number of infections and deaths could be 6.5 (90% CI: 1.3-21) and 7.9 (90% CI: 1.5-23) times higher, respectively, in comparison with the actual implementation of AE. CONCLUSIONS: Our results suggest that the AE implemented in Brazil had a significant influence on social isolation by allowing those in need to stay at home, which would reduce the expected numbers of infections and deaths.

Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply.

BACKGROUND: At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. METHODS: We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. RESULTS: The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. CONCLUSIONS: Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

COVID-19 underreporting and its impact on vaccination strategies.

BACKGROUND: Underreporting cases of infectious diseases poses a major challenge in the analysis of their epidemiological characteristics and dynamical aspects. Without accurate numerical estimates it is difficult to precisely quantify the proportions of severe and critical cases, as well as the mortality rate. Such estimates can be provided for instance by testing the presence of the virus. However, during an ongoing epidemic, such tests' implementation is a daunting task. This work addresses this issue by presenting a methodology to estimate underreported infections based on approximations of the stable rates of hospitalization and death. METHODS: We present a novel methodology for the stable rate estimation of hospitalization and death related to the Corona Virus Disease 2019 (COVID-19) using publicly available reports from various distinct communities. These rates are then used to estimate underreported infections on the corresponding areas by making use of reported daily hospitalizations and deaths. The impact of underreporting infections on vaccination strategies is estimated under different disease-transmission scenarios using a Susceptible-Exposed-Infective-Removed-like (SEIR) epidemiological model. RESULTS: For the considered locations, during the period of study, the estimations suggest that the number of infected individuals could reach 30% of the population of these places, representing, in some cases, more than six times the observed numbers. These results are in close agreement with estimates from independent seroprevalence studies, thus providing a strong validation of the proposed methodology. Moreover, the presence of large numbers of underreported infections can reduce the perceived impact of vaccination strategies in reducing rates of mortality and hospitalization. CONCLUSIONS: pBy using the proposed methodology and employing a judiciously chosen data analysis implementation, we estimate COVID-19 underreporting from publicly available data. This leads to a powerful way of quantifying underreporting impact on the efficacy of vaccination strategies. As a byproduct, we evaluate the impact of underreporting in the designing of vaccination strategies.

Estimating the effects of reopening of schools on the course of the epidemic of COVID-19.

In this paper, we present a method to estimate the risk of reopening of schools illustrated with the case of the State of São Paulo, Brazil. The model showed that, although no death of children would result from the reopening of the schools in the three cities analysed, the risk of asymptomatic and symptomatic cases and secondary cases among teachers, school staff and relatives of the children is not negligible. Although the epidemic hit different regions with different intensities, our model shows that, for regions where the incidence profile is similar to the cities analysed, the risk of reopening of schools is still too high. This in spite of the fact that incidences in these cities were declining in the period of the time considered. Therefore, although we cannot extend the result to the entire country, the overall conclusion is valid for regions with a declining incidence and it is even more valid for regions where incidence is increasing. We assumed a very conservative level of infection transmissibility of children of just 10% as that of adults. In spite of the very low level of transmissibility is assumed, the number of secondary cases caused by infected children among teachers, school staff and relatives varied from 2 to 85. It is, therefore, too soon to have any degree of confidence that reopening of schools before the advent of a vaccine is the right decision to take. The purpose of our model and simulations is to provide a method to estimate the risk of school reopening, although we are sure it could be applied as a guide to public health strategies.

Public health messages on arboviruses transmitted by Aedes aegypti in Brazil.

BACKGROUND: The outbreak of Zika virus in Brazil in 2015 followed the arrival of chikungunya in 2014 and a long history of dengue circulation. Vital to the response to these outbreaks of mosquito-borne pathogens has been the dissemination of public health messages, including those promoted through risk communication posters. This study explores the content of a sample of posters circulated in Brazil towards the end of the Zika epidemic in 2017 and analyses their potential effectiveness in inducing behaviour change. METHODS: A content analysis was performed on 37 posters produced in Brazil to address outbreaks of mosquito-borne pathogens. The six variables of the Health Belief Model were used to assess the potential effectiveness of the posters to induce behaviour change. RESULTS: Three overarching key messages emerged from the posters. These included (i) the arboviruses and their outcomes, (ii) a battle against the mosquito, and (iii) a responsibility to protect and prevent. Among the six variables utilised through the Health Belief Model, cues to action were most commonly featured, whilst the perceived benefits of engaging in behaviours to prevent arbovirus transmission were the least commonly featured. CONCLUSIONS: The posters largely focused on mosquito-borne transmission and the need to eliminate breeding sites, and neglected the risk of the sexual and congenital transmission of Zika and the importance of alternative preventive actions. This, we argue, may have limited the potential effectiveness of these posters to induce behaviour change.

Modelling the effect of a dengue vaccine on reducing the evolution of resistance against antibiotic due to misuse in dengue cases.

BACKGROUND: This paper intends to check whether and how a hypothetical dengue vaccine could contribute to issue of evolution of bacteria resistance against antibiotics by reducing the number of patients that would inappropriately being treated with antibiotics. METHODS: We use a new mathematical model that combines, in a novel way, two previously published papers, one on the evolution of resistance against antibiotics and one classical Ross-Macdonald model for dengue transmission. RESULTS: The model is simulated numerically and reproduces a real case of evolution of resistance against antibiotics. In addition the model shows that the use of a hypothetical dengue vaccine could help to curb the evolution of resistance against an antibiotic inappropriately used in dengue patients. Both the increase in the proportion of resistant bacteria due to the misuse of antibiotics in dengue cases as a function of the fraction of treated patients and the reduction of that proportion as a function of vaccination coverage occur in a highly non-linear fashion. CONCLUSION: The use of a dengue vaccine is helpful in reducing the rate of evolution of antibiotic resistance in a scenario of misuse of the antibiotics in dengue patients.

Two complementary model-based methods for calculating the risk of international spreading of a novel virus from the outbreak epicentre. The case of COVID-19.

We present two complementary model-based methods for calculating the risk of international spread of the novel coronavirus SARS-CoV-2 from the outbreak epicentre. One model aims to calculate the number of cases that would be exported from an endemic country to disease-free regions by travellers. The second model calculates the probability that an infected traveller will generate at least one secondary autochthonous case in the visited country. Although this paper focuses on the data from China, our methods can be adapted to calculate the risk of importation and subsequent outbreaks. We found an average R0 = 5.31 (ranging from 4.08 to 7.91) and a risk of spreading of 0.75 latent individuals per 1000 travellers. In addition, one infective traveller would be able to generate at least one secondary autochthonous case in the visited country with a probability of 23%.

The Optimal Age of Vaccination Against Dengue with an Age-Dependent Biting Rate with Application to Brazil.

In this paper we introduce a single serotype transmission model, including an age-dependent mosquito biting rate, to find the optimal vaccination age against dengue in Brazil with Dengvaxia. The optimal vaccination age and minimal lifetime expected risk of hospitalisation are found by adapting a method due to Hethcote (Math Biosci 89:29-52). Any number and combination of the four dengue serotypes DENv1-4 is considered. Successful vaccination against a serotype corresponds to a silent infection. The effects of antibody-dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections are studied. ADE is assumed to imply risk-free primary infections, while permanent cross-immunity implies risk-free tertiary and quaternary infections. Data from trials of Dengvaxia indicate vaccine efficacy to be age and serostatus dependent and vaccination of seronegative individuals to induce an increased risk of hospitalisation. Some of the scenarios are therefore reconsidered taking these findings into account. The optimal vaccination age is compared to that achievable under the current age restriction of the vaccine. If vaccination is not considered to induce risk, optimal vaccination ages are very low. The assumption of ADE generally leads to a higher optimal vaccination age in this case. For a single serotype vaccination is not recommended in the case of ADE. Permanent cross-immunity results in a slightly lower optimal vaccination age. If vaccination induces a risk, the optimal vaccination ages are much higher, particularly for permanent cross-immunity. ADE has no effect on the optimal vaccination age when permanent cross-immunity is considered; otherwise, it leads to a slight increase in optimal vaccination age.

Vector competence, vectorial capacity of Nyssorhynchus darlingi and the basic reproduction number of Plasmodium vivax in agricultural settlements in the Amazonian Region of Brazil.

BACKGROUND: Brazilian malaria control programmes successfully reduced the incidence and mortality rates from 2005 to 2016. Since 2017, increased malaria has been reported across the Amazon. Few field studies focus on the primary malaria vector in high to moderate endemic areas, Nyssorhynchus darlingi, as the key entomological component of malaria risk, and on the metrics of Plasmodium vivax propagation in Amazonian rural communities. METHODS: Human landing catch collections were carried out in 36 houses of 26 communities in five municipalities in the Brazilian states of Acre, Amazonas and Rondônia states, with API (> 30). In addition, data on the number of locally acquired symptomatic infections were employed in mathematical modelling analyses carried out to determine Ny. darlingi vector competence and vectorial capacity to P. vivax; and to calculate the basic reproduction number for P. vivax. RESULTS: Entomological indices and malaria metrics ranged among localities: prevalence of P. vivax infection in Ny. darlingi, from 0.243% in Mâncio Lima, Acre to 3.96% in Machadinho D'Oeste, Rondônia; daily human-biting rate per person from 23 ± 1.18 in Cruzeiro do Sul, Acre, to 66 ± 2.41 in Lábrea, Amazonas; vector competence from 0.00456 in São Gabriel da Cachoeira, Amazonas to 0.04764 in Mâncio Lima, Acre; vectorial capacity from 0.0836 in Mâncio Lima, to 1.5 in Machadinho D'Oeste. The estimated R0 for P. vivax (PvR0) was 3.3 in Mâncio Lima, 7.0 in Lábrea, 16.8 in Cruzeiro do Sul, 55.5 in São Gabriel da Cachoeira, and 58.7 in Machadinho D'Oeste. Correlation between P. vivax prevalence in Ny. darlingi and vector competence was non-linear whereas association between prevalence of P. vivax in mosquitoes, vectorial capacity and R0 was linear and positive. CONCLUSIONS: In spite of low vector competence of Ny. darlingi to P. vivax, parasite propagation in the human population is enhanced by the high human-biting rate, and relatively high vectorial capacity. The high PvR0 values suggest hyperendemicity in Machadinho D'Oeste and São Gabriel da Cachoeira at levels similar to those found for P. falciparum in sub-Saharan Africa regions. Mass screening for parasite reservoirs, effective anti-malarial drugs and vector control interventions will be necessary to shrinking transmission in Amazonian rural communities, Brazil.

Modelling an optimum vaccination strategy against ZIKA virus for outbreak use.

We present a model to optimise a vaccination campaign aiming to prevent or to curb a Zika virus outbreak. We show that the optimum vaccination strategy to reduce the number of cases by a mass vaccination campaign should start when the Aedes mosquitoes' density reaches the threshold of 1.5 mosquitoes per humans, the moment the reproduction number crosses one. The maximum time it is advisable to wait for the introduction of a vaccination campaign is when the first ZIKV case is identified, although this would not be as effective to minimise the number of infections as when the mosquitoes' density crosses the critical threshold. This suboptimum strategy, however, would still curb the outbreak. In both cases, the catch up strategy should aim to vaccinate at least 25% of the target population during a concentrated effort of 1 month immediately after identifying the threshold. This is the time taken to accumulate the herd immunity threshold of 56.5%. These calculations were done based on theoretical assumptions that vaccine implementation would be feasible within a very short time frame.

Projecting the end of the Zika virus epidemic in Latin America: a modelling analysis.

BACKGROUND: Zika virus (ZIKV) emerged in Latin America and the Caribbean (LAC) region in 2013, with serious implications for population health in the region. In 2016, the World Health Organization declared the ZIKV outbreak a Public Health Emergency of International Concern following a cluster of associated neurological disorders and neonatal malformations. In 2017, Zika cases declined, but future incidence in LAC remains uncertain due to gaps in our understanding, considerable variation in surveillance and the lack of a comprehensive collation of data from affected countries. METHODS: Our analysis combines information on confirmed and suspected Zika cases across LAC countries and a spatio-temporal dynamic transmission model for ZIKV infection to determine key transmission parameters and projected incidence in 90 major cities within 35 countries. Seasonality was determined by spatio-temporal estimates of Aedes aegypti vectorial capacity. We used country and state-level data from 2015 to mid-2017 to infer key model parameters, country-specific disease reporting rates, and the 2018 projected incidence. A 10-fold cross-validation approach was used to validate parameter estimates to out-of-sample epidemic trajectories. RESULTS: There was limited transmission in 2015, but in 2016 and 2017 there was sufficient opportunity for wide-spread ZIKV transmission in most cities, resulting in the depletion of susceptible individuals. We predict that the highest number of cases in 2018 would present within some Brazilian States (Sao Paulo and Rio de Janeiro), Colombia and French Guiana, but the estimated number of cases were no more than a few hundred. Model estimates of the timing of the peak in incidence were correlated (p < 0.05) with the reported peak in incidence. The reporting rate varied across countries, with lower reporting rates for those with only confirmed cases compared to those who reported both confirmed and suspected cases. CONCLUSIONS: The findings suggest that the ZIKV epidemic is by and large over within LAC, with incidence projected to be low in most cities in 2018. Local low levels of transmission are probable, but the estimated rate of infection suggests that most cities have a population with high levels of herd immunity.

Using the human blood index to investigate host biting plasticity: a systematic review and meta-regression of the three major African malaria vectors.

BACKGROUND: The proportion of mosquito blood-meals that are of human origin, referred to as the 'human blood index' or HBI, is a key determinant of malaria transmission. METHODS: A systematic review was conducted followed by meta-regression of the HBI for the major African malaria vectors. RESULTS: Evidence is presented for higher HBI among Anopheles gambiae (M/S forms and Anopheles coluzzii/An. gambiae sensu stricto are not distinguished for most studies and, therefore, combined) as well as Anopheles funestus when compared with Anopheles arabiensis (prevalence odds ratio adjusted for collection location [i.e. indoor or outdoor]: 1.62; 95% CI 1.09-2.42; 1.84; 95% CI 1.35-2.52, respectively). This finding is in keeping with the entomological literature which describes An. arabiensis to be more zoophagic than the other major African vectors. However, analysis also revealed that HBI was more associated with location of mosquito captures (R2 = 0.29) than with mosquito (sibling) species (R2 = 0.11). CONCLUSIONS: These findings call into question the appropriateness of current methods of assessing host preferences among disease vectors and have important implications for strategizing vector control.

Is vaccinating monkeys against yellow fever the ultimate solution for the Brazilian recurrent epizootics?

Vaccinating monkeys against yellow fever (YF) has been a common practice in the beginning of the 17D vaccine development. Although it may seem strange at first sight, vaccinating monkeys as a public health strategy is, we think, feasible and theoretically could eliminate the infection among non-human primates, interrupting the virus circulation (or significantly reducing it) and therefore reducing the risk of spilling over to the human population. We propose a series of studies that could demonstrate (or not) the efficacy and feasibility of vaccinating non-human primates YF reservoirs living in green areas of urban centres to cut off or curb the virus circulation that recurrently spill over to the human population. Therefore, vaccinating monkeys in relatively small green areas of the urban centres is perhaps the ultimate solution for the Brazilian recurrent YF epizootics.

The risk of urban yellow fever resurgence in Aedes-infested American cities.

Aedes aegypti, historically known as yellow fever (YF) mosquito, transmits a great number of other viruses such as Dengue, West Nile, Chikungunya, Zika, Mayaro and perhaps Oropouche, among others. Well established in Africa and Asia, Aedes mosquitoes are now increasingly invading large parts of the American continent, and hence the risk of urban YF resurgence in the American cities should because of great concern to public health authorities. Although no new urban cycle of YF was reported in the Americas since the end of an Aedes eradication programme in the late 1950s, the high number of non-vaccinated individuals that visit endemic areas, that is, South American jungles where the sylvatic cycle of YF is transmitted by canopy mosquitoes, and return to Aedes-infested urban areas, increases the risk of resurgence of the urban cycle of YF. We present a method to estimate the risk of urban YF resurgence in dengue-endemic cities. This method consists in (1) to estimate the number of Aedes mosquitoes that explains a given dengue outbreak in a given region; (2) calculate the force of infection caused by the introduction of one infective individual per unit area in the endemic area under study; (3) using the above estimates, calculate the probability of at least one autochthonous YF case per unit area produced by one single viraemic traveller per unit area arriving from a YF endemic or epidemic sylvatic region at the city studied. We demonstrate that, provided the relative vector competence, here defined as the capacity to being infected and disseminate the virus, of Ae. aegypti is greater than 0.7 (with respect to dengue), one infected traveller can introduce urban YF in a dengue endemic area.

Modelling the impact of the long-term use of insecticide-treated bed nets on Anopheles mosquito biting time.

BACKGROUND: Evidence of changing in biting and resting behaviour of the main malaria vectors has been mounting up in recent years as a result of selective pressure by the widespread and long-term use of insecticide-treated bed nets (ITNs), and indoor residual spraying. The impact of resistance behaviour on malaria intervention efficacy has important implications for the epidemiology and malaria control programmes. In this context, a theoretical framework is presented to understand the mechanisms determining the evolution of feeding behaviour under the pressure of use of ITNs. METHODS: An agent-based stochastic model simulates the impact of insecticide-treated bed nets on mosquito fitness by reducing the biting rates, as well as increasing mortality rates. The model also incorporates a heritability function that provides the necessary genetic plasticity upon which natural selection would act to maximize the fitness under the pressure of the control strategy. RESULTS: The asymptotic equilibrium distribution of mosquito population versus biting time is shown for several daily uses of ITNs, and the expected disruptive selection on this mosquito trait is observed in the simulations. The relative fitness of strains that bite at much earlier time with respect to the wild strains, when a threshold of about 50% of ITNs coverage highlights the hypothesis of a behaviour selection. A sensitivity analysis has shown that the top three parameters that play a dominant role on the mosquito fitness are the proportion of individuals using bed nets and its effectiveness, the impact of bed nets on mosquito oviposition, and the mosquito genetic plasticity related to changing in biting time. CONCLUSION: By taking the evolutionary aspect into account, the model was able to show that the long-term use of ITNs, although representing an undisputed success in reducing malaria incidence and mortality in many affected areas, is not free of undesirable side effects. From the evolutionary point of view of the parasite virulence, it should be expected that plasmodium parasites would be under pressure to reduce their virulence. This speculative hypothesis can eventually be demonstrated in the medium to long-term use of ITNs.

Estimating the prevalence of infectious diseases from under-reported age-dependent compulsorily notification databases.

BACKGROUND: National or local laws, norms or regulations (sometimes and in some countries) require medical providers to report notifiable diseases to public health authorities. Reporting, however, is almost always incomplete. This is due to a variety of reasons, ranging from not recognizing the diseased to failures in the technical or administrative steps leading to the final official register in the disease notification system. The reported fraction varies from 9 to 99% and is strongly associated with the disease being reported. METHODS: In this paper we propose a method to approximately estimate the full prevalence (and any other variable or parameter related to transmission intensity) of infectious diseases. The model assumes incomplete notification of incidence and allows the estimation of the non-notified number of infections and it is illustrated by the case of hepatitis C in Brazil. The method has the advantage that it can be corrected iteratively by comparing its findings with empirical results. RESULTS: The application of the model for the case of hepatitis C in Brazil resulted in a prevalence of notified cases that varied between 163,902 and 169,382 cases; a prevalence of non-notified cases that varied between 1,433,638 and 1,446,771; and a total prevalence of infections that varied between 1,597,540 and 1,616,153 cases. CONCLUSIONS: We conclude that the model proposed can be useful for estimation of the actual magnitude of endemic states of infectious diseases, particularly for those where the number of notified cases is only the tip of the iceberg. In addition, the method can be applied to other situations, such as the well-known underreported incidence of criminality (for example rape), among others.

The risk of dengue for non-immune foreign visitors to the 2016 summer olympic games in Rio de Janeiro, Brazil.

BACKGROUND: Rio de Janeiro in Brazil will host the Summer Olympic Games in 2016. About 400,000 non-immune foreign tourists are expected to attend the games. As Brazil is the country with the highest number of dengue cases worldwide, concern about the risk of dengue for travelers is justified. METHODS: A mathematical model to calculate the risk of developing dengue for foreign tourists attending the Olympic Games in Rio de Janeiro in 2016 is proposed. A system of differential equation models the spread of dengue amongst the resident population and a stochastic approximation is used to assess the risk to tourists. Historical reported dengue time series in Rio de Janeiro for the years 2000-2015 is used to find out the time dependent force of infection, which is then used to estimate the potential risks to a large tourist cohort. The worst outbreak of dengue occurred in 2012 and this and the other years in the history of Dengue in Rio are used to discuss potential risks to tourists amongst visitors to the forthcoming Rio Olympics. RESULTS: The individual risk to be infected by dengue is very much dependent on the ratio asymptomatic/symptomatic considered but independently of this the worst month of August in the period studied in terms of dengue transmission, occurred in 2007. CONCLUSIONS: If dengue returns in 2016 with the pattern observed in the worst month of August in history (2007), the expected number of symptomatic and asymptomatic dengue cases among tourists will be 23 and 206 cases, respectively. This worst case scenario would have an incidence of 5.75 (symptomatic) and 51.5 (asymptomatic) per 100,000 individuals.