Analysis of the Impact of Vaccination as Control Strategy of Dengue Transmission Dynamics Considering a Multi-Strain Model

Abstract

Optimizing a strategy for Dengue control based on vaccination is very challenging, since the dynamics of Dengue can be influenced by the coexistence of more than one serotype (DENV-1, DENV-2, DENV-3 and DENV-4), allowing the appearance of heterologous infections. In addition, although the effect of cross-immunity lasts a short period, the real protective power of the immune response is still not entirely clear. The aim of this study is to develop an optimization model to control Dengue transmission considering a multi-strain model. In order to evaluate such optimization, the vaccination was considered the control strategy. The Dengue dynamics was modeled according to that one developed by [1]. This model considered a human population, which can be infected by two strains of Dengue virus (strain 1 and 2). Both strains are simultaneously present in the system and they determine 10 categories in human population: susceptible to strains 1 and 2 (); primarily infected with strain 1 () or strain 2 (); recovered from the first infection with strain 1 () or strain 2 (); susceptible with a previous infection with strain 1 () or strain 2 (); secondarily infected with strain 1, when the first infection was caused by strain 2 () or for second time infected with strain 2 when the first infection was caused by strain 1 (); recovered from the secondary infection (). Initially, with the purpose of understand the Dengue dynamics in such conditions, the model was simulated without the introduction of vaccination. Following, the vaccination was introduced in this model. Although the vaccination was distributed to whole population, the vaccination effects occurs only on individual of category (the vaccinated individuals from move to category). Once in this category, individuals can become infected due to vaccination, moving to category. Otherwise, they become successfully protected (). Once the same individual cannot become infected by two different serotypes at the same time, there will be a competition between serotypes 1 and 2. However, the vaccination does not decrease the serotype 1 infected individuals, because there would be more susceptible individual's available to be infected by serotype 1. In other words, the serotype 1 would prevail in this population.