Analysis of dengue vaccine through an age-structured model using actual epidemics data

Many efforts have been done in the last years for the development of a tetravalent vaccine against dengue. It is expected that, at the very beginning of vaccination campaigns, there won't be enough vaccines for the whole population. Therefore, mathematical modelling is a very important tool to exhibit different scenarios concerning the most efficient strategy to avoid epidemics, i.e., to reduce the basic reproductive number R0 below unit. In this work, inspired by the literature[1], we propose a model with age structure for human compartments (1-9, 10-19, 20-29, 30-39, 40-49, 50-59, over 60) and homogeneous for vector compartiments, assuming continuous vaccination. The infection rate values are based on the force of infection for different age ranges of actual epidemics occurred in some Brazilian cities: Fortaleza (2008), Goi?nia (2010), Manaus (2011), and Rio de Janeiro (2008). The chosen epidemics presents, for each city, the highest peak of dengue cases. We obtain analitically the expressions of global R0 and R0 for each age range [2] and calculate their values for those epidemics. According to these previous scenarios, we conclude that the best strategy to reduce the global R0 of Fortaleza, Goi?nia and Manaus is to vaccinate children who are 1 to 9 years old. For Rio de Janeiro it is better to vaccinate people of 2 age ranges: children who are 1 to 9 years old and children and teenagers who are 10 to 19 years old. If the vaccine efficacy is about 60.8$\%$, we obtain that it is enough to innoculate 3$\%$, 4$\%$ and 4$\%$ per week of children who are 1 to 9 years old in Fortaleza, Goi?nia and Manaus respectively. In Rio de Janeiro 1$\%$ per week of people who are 1 to 19 years old would have to be vaccinated. Furthermore, we intend to find the minimal proportion of vaccinated people necessary to avoid epidemics, assuming a vaccination campaign instead of continuous vaccination. Finally it would be interesting to extend that analysis to other cities as well as to analyse the effective reproduction number.

[1] Tasman H, Supriatna AK, Nuraini N, Soewono E. A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population. Int. J. Math. Mathl. Sci., 2012: 1-15, 2012.

[2] Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180: 29-48, 2002.