Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic

OBJECTIVES: With the declining numbers of coronavirus disease 2019 (COVID-19) cases in the state of São Paulo, Brazil, social distancing measures have gradually been lifted. However, the risk of a surge in the number of cases cannot be overlooked. Even with the adoption of nonpharmaceutical interventions, such as restrictions on mass gatherings, wearing of masks, and complete or partial closure of schools, other public health measures may help control the epidemic. We aimed to evaluate the impact of the contact tracing of symptomatic individuals on the COVID-19 epidemic regardless of the use of diagnostic testing. METHODS: We developed a mathematical model that includes isolation of symptomatic individuals and tracing of contacts to assess the effects of the contact tracing of symptomatic individuals on the COVID-19 epidemic in the state of São Paulo. RESULTS: For a selection efficacy (proportion of isolated contacts who are infected) of 80%, cases and deaths may be reduced by 80% after 60 days when 5000 symptomatic individuals are isolated per day, each of them together with 10 contacts. On the other hand, for a selection efficacy of 20%, the number of cases and deaths may be reduced by approximately 40% and 50%, respectively, compared with the scenario in which no contact-tracing strategy is implemented. CONCLUSION: Contact tracing of symptomatic individuals may potentially be an alternative strategy when the number of diagnostic tests available is not sufficient for massive testing.

A public health risk assessment for yellow fever vaccination: a model exemplified by an outbreak in the state of São Paulo, Brazil

We propose a method to analyse the 2009 outbreak in the region of Botucatu in the state of São Paulo (SP), Brazil, when 28 yellow fever (YF) cases were confirmed, including 11 deaths. At the time of the outbreak, the Secretary of Health of the State of São Paulo vaccinated one million people, causing the death of five individuals, an unprecedented number of YF vaccine-induced fatalities. We apply a mathematical model described previously to optimise the proportion of people who should be vaccinated to minimise the total number of deaths. The model was used to calculate the optimum proportion that should be vaccinated in the remaining, vaccine-free regions of SP, considering the risk of vaccine-induced fatalities and the risk of YF outbreaks in these regions.

Risk of symptomatic dengue for foreign visitors to the 2014 FIFA World Cup in Brazil

Brazil will host the FIFA World Cup™, the biggest single-event competition in the world, from June 12-July 13 2014 in 12 cities. This event will draw an estimated 600,000 international visitors. Brazil is endemic for dengue. Hence, attendees of the 2014 event are theoretically at risk for dengue. We calculated the risk of dengue acquisition to non-immune international travellers to Brazil, depending on the football match schedules, considering locations and dates of such matches for June and July 2014. We estimated the average per-capita risk and expected number of dengue cases for each host-city and each game schedule chosen based on reported dengue cases to the Brazilian Ministry of Health for the period between 2010-2013. On the average, the expected number of cases among the 600,000 foreigner tourists during the World Cup is 33, varying from 3-59. Such risk estimates will not only benefit individual travellers for adequate pre-travel preparations, but also provide valuable information for public health professionals and policy makers worldwide. Furthermore, estimates of dengue cases in international travellers during the World Cup can help to anticipate the theoretical risk for exportation of dengue into currently non-infected areas.

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

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

The risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA

We estimate the risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA. This is done by a mathematical model that quantifies the intensity of transmission of the new virus in those countries and the probability that one individual has of acquiring the influenza depending on the date of arrival and time spent in the area. The maximum estimated risk reached 7.5 cases per 10,000 visitors to Chile, 17 cases per 10,000 travelers to Argentina and 23 cases per 10,000 travelers to the USA. The estimated number of imported cases until 27 July is 57 ± 9 from Chile, 136 ± 27 from the USA and 301 ± 21 from Argentina, which are in accord with the official figures. Estimating the number of imported cases was particularly important for the moment of the disease introduction into this country, but it will certainly be important again as a tool to calculate the number of future imported cases from northern countries in our next inter-epidemic season, were imported cases can constitute again the majority of the new influenza burden to the Brazilian health services.

Dynamics of the 2006/2007 dengue outbreak in Brazil

We analyzed dengue incidence in the period between October 2006-July 2007 of 146 cities around the country were Larval Index Rapid Assay (LIRA) surveillance was carried out in October 2006. Of these, we chosen 61 cities that had 500 or more cases reported during this period. We calculated the incidence coefficient, the force of infection (¼) and the basic reproduction number (R0) of dengue in those 61 cities and correlated those variables with the LIRA. We concluded that ¼ and R0 are more associated with the number of cases than LIRA. In addition, the average R0 for the 2006/2007 dengue season was almost as high as that calculated for the 2001/2002 season, the worst in Brazilian history.

Dengue and the risk of urban yellow fever reintroduction in Säo Paulo State, Brazil

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 säo transmitidas pelo mesmo vetor (Aedes aegypti), poder-se-ia 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. Demonstra-se que o R0 da febre amarela é em média 43por cento menor que o da dengue. Esta diferença deve-se à viremia mais prolongada da dengue, bem como ao menor período de incubaçäo extrínseco daquele vírus no mosquito. RESULTADOS: Apresenta-se a aplicaçäo desta análise matemática à situaçäo epidemiológica da dengue no estado de Säo Paulo, para o ano de 2001, onde o número de casos de dengue aumentou de 3.582, em 2000 para 51.348, em 2001. Calculou-se o valor de R0 para a febre amarela para cada cidade do estado que tinha R0 para dengue maior que um. Estimou-se o número total de pessoas desprotegidas, sem vacina, e que vivem em áreas de alto risco para a febre amarela urbana. CONCLUSOES: Foi demonstrado que existe, um grande contingente de pessoas näo vacinadas contra febre amarela vivendo em áreas infestadas por Aedes aegypti no Estado de Säo Paulo, até aquela data (2001)