Analysis of the optimal vaccination age for dengue in Brazil with a tetravalent dengue vaccine

Abstract

Highlights• Mathematical model to analyse the optimal vaccination age against Dengue in Brazil.• Use epidemiological data from Brazil.• Consider both hospitalisation and lethality risks.• Model possible Dengue Antibody Enhancement.• Calculations repeated with third and fourth infections asymptomatic. AbstractIn this paper we study a mathematical model to analyse the optimal vaccination age against Dengue in Brazil. Data from Brazil are used to estimate the basic reproduction numbers for each of the four Dengue serotypes and then the optimal vaccination age is calculated using a method due to Hethcote [1]. The vaccine has different efficacies against each serotype. Vaccination that is too early is ineffective as individuals are protected by maternal antibodies but leaving vaccination until later may allow the disease to spread.First of all the optimal vaccination ages are calculated where there is just one serotype in circulation and then when there are multiple serotypes. The calculations are done using data both assuming constant vaccine efficacy and agedependent vaccine efficacy against a given serotype. The multiple serotype calculations are repeated assuming that the first infection is a risky infection and that it is not (to model Dengue Antibody Enhancement). The calculations are then repeated when any third or fourth Dengue infections are asymptomatic, so that two Dengue infections with different serotypes provide effective permanent immunity. The calculations are also repeated when the age-dependent risk function (fitted to Brazilian data) is hospitalisation from Dengue and when it is mortality due to Dengue. We find a wide variety of optimal vaccination ages depending on both the serotypes in circulation and the assumptions of the model.

System of delay differential equations with application in dengue fever

“…recovery time 4 − 10 days (Gubler, 2014;WHO, 2009) 1 ω i cross immunity protection time 2 − 9 months (Gubler, 2014;WHO, 2009) Ferguson, 1999a) These values were calculated in order to give reasonable Basic Reproduction numbers for Dengue. For instance, Maier (2017) and Massad (2001) have estimated the range of of the values for the parameter is in accordance to the values found in the study by Kooi (2014),…”

Parameter fitting using time-scale analysis for vector-borne diseases with spatial dynamics

“…More recently, control measures with Wolbachia 21 bacteria have also been successfully tested, which prevents the vector from transmitting 22 the virus [11,12]. Some vaccines have been tested and others are in testing phase, but 23 the greatest difficulty is that such vaccines should be tetravalent, that is, they must be 24 effective against the 4 existing serotypes of the disease [13,14]. 25 Mathematical models used to describe indirectly transmitted infectious diseases have 26 the interesting characteristic of coupling the dynamics of hosts and vectors, whose 27 parameters have different time scales, the life cycle of mosquitoes is in days while 28 humans life cycle is in years.…”

Modelos para a dinâmica da dengue com infecção sequencial e inclusão de estratégias de vacinação por vacina tetravalente

“…Evidências de que a incidência de dengue mudou ao longo dos anos, por exemplo, no Brasil, tem atingido mais crianças ultimamente (Rodriguez-Barraquer et al, 2011), fez com que modelos fossem adaptados para considerar os diferentes fatores que inuenciam na vacinação como: estrutura de idade, proporção da população a ser vacinada, suscetibilidade da população, ecácia da vacina e melhor idade para aplicá-la (Anderson e May, 1985Andraud et al, 2012;d'Onofrio, 2002; xxi Ferguson et al, 1999b;Gjini et al, 2016;Gomes et al, 2004Gomes et al, , 2014Liu et al, 2008;Maier et al, 2017;Martcheva, 2015;Massad et al, 1994;Rodrigues et al, 2014). Alguns trabalhos também analisam os impactos dos programas de vacinação, mostrando que dependendo do nível de redução do vetor há um limiar na ecácia da vacina abaixo do qual é melhor não introduzi-la (Boccia et al, 2014;Scherer e McLean, 2002).…”

“…Alguns trabalhos também analisam os impactos dos programas de vacinação, mostrando que dependendo do nível de redução do vetor há um limiar na ecácia da vacina abaixo do qual é melhor não introduzi-la (Boccia et al, 2014;Scherer e McLean, 2002). Modelos atuais estão sendo aperfeiçoados para analisar o resultado de aplicação de vacinas desenvolvidas para a dengue, devido ao fato desta oferecer proteção contra os 4 sorotipos existentes, como as vacinas do Sano e do Instituto Butantan (Aguiar et al, 2016;Billings et al, 2008;Ferguson et al, 2016;Maier et al, 2017;Precioso et al, 2015). A vacina do Sano foi mostrada ter boa ecácia se aplicada em indivíduos de 9 a 45 anos e que já tiveram infecção previamente (Aguiar et al, 2016;, aumentando o risco de hospitalização em indivíduos soronegativos, enquanto a vacina do Instituto Butantan está na fase de testes III (Precioso et al, 2015).…”

“…A maior diculdade no processo de vacinação é lidar com o fato de que é muito difícil produzir uma vacina 100 % ecaz. A esperança é que a vacina forneça imunidade de longa duração à infecção e previna ambos a transmissão e os sintomas da doença (Anderson e May, 1985Billings et al, 2008;d'Onofrio, 2002;Gomes et al, 2004Gomes et al, , 2014Keeling e Rohani, 2008;Liu et al, 2008;Maier et al, 2017;Massad et al, 1994;Rodrigues et al, 2013;Scherer e McLean, 2002;Yang, 2001).…”