Mathematical modeling of dengue epidemic: control methods and vaccination strategies

Abstract

Dengue is one of the most important infectious diseases in the world, in terms of death and economic cost. Hence, the modeling of dengue is of great importance to help us understand the dynamics disease, and interfering with its spreading mathematical by the proposition of control methods. In this work, control strategies in an attempt to eliminate the Aedes aegypti mosquito, as well as proposals for the vaccination campaign are evaluated. In our mathematical model, the mechanical control is accomplished through the environmental support capacity affected by a discrete function that represents removal of breeding. Chemical control is carried out from the use of insecticide and larvicidal. The efficacious of vaccination is studied through the removal of a fraction of individuals, proportional to the rate of vaccination, from the susceptible compartment and its transfer to the recovered compartment. Our major find is that the dengue fever epidemic is only eradicated with the use of an immunizing vaccine because control measures directed against the vector are not enough to halt disease spreading. Even where the infected mosquitoes are eliminated from the system, susceptible mosquitoes are still present, and infected humans cause dengue fever to reappear in the human population.

Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases

“…In line with Yang and Ferreira [67], Dumont and Chiroleu [23], and Carvalho et al [13], we compare the effects of different strategies applied on the arboviral diseases, by the introduction of the efficiency index, designed by F. To this aim, we define the variable A as the area comprised between the curve of the symptomatic infectious human (I h ) population size, for instance, and the time axis during the period of time from 0 to t f , as…”

“…which measures the cumulated number of infectious human during the time interval [0, t f ] [13,67]. Hence the efficiency index, F, be can defined by…”

“…The dynamics of arboviral diseases like Dengue or Chikungunya are influenced by many factors such as human and mosquito behaviours. The virus itself (multiple serotypes of dengue virus [65,64], and multiple strains of chikungunya virus [22,46]), as well as the environment, affects directly or indirectly all the present mechanisms of control [5,13]. Indeed, in the absence of conditions which favour the development of their larvae, eggs of certain Aedes mosquitoes (Aedes albopictus, for example) enter in diapause phenomenon, allowing the eggs to hatch even after two years [47,57].…”

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

“…But, if we use only one control among u 1 and u 2 then one question may arise 'which control is more efficient to reduce infection ?' To answer this question we will perform an efficiency analysis [17] which will allow us to determine the best control strategy. Here, we distinguish two control strategies STR-1 and STR-2 where STR-1 is the strategy where u 1 = 0 , u 2 = 0 and STR-2 is the strategy where u 1 = 0 , u 2 = 0.…”

“…where A c and A o are the cumulated number of infected individuals with and without control, respectively. The best strategy will be the one whom efficiency index will be bigger [17]. It can be noted that the cumulated number of infected individuals during the time interval [0, 20] is defined by A = 20 0 I(t)dt.…”