Multiobjective optimization to assess dengue control costs using a climate-dependent epidemiological model

Abstract

Arboviruses, diseases transmitted by arthropods, have become a significant challenge for public health managers. The World Health Organization highlights dengue as responsible for millions of infections worldwide annually. As there is no specific treatment for the disease and no free-of-charge vaccine for mass use in Brazil, the best option is the measures to combat the vector, the Aedes aegypti mosquito. Therefore, we proposed an epidemiological model dependent on temperature, precipitation, and humidity, considering symptomatic and asymptomatic dengue infections. Through computer simulations, we aimed to minimize the amount of insecticides and the social cost demanded to treat patients. We proposed a case study in which our model is fitted with real data from symptomatic dengue-infected humans in an epidemic year in a Brazilian city. Our multiobjective optimization model considers an additional control using larvicide, adulticide, and ultra-low volume spraying. The work's main contribution is studying the monetary cost of the actions to combat the vector demand versus the hospital cost per confirmed infected, comparing approaches with and without additional control. Results showed that the additional vector control measures are cheaper than the hospital treatment without the vector control would be.

Figure 1

Location of the city of Belo Horizonte in the State of Minas Gerais and its series of precipitation, temperature, and humidity. The map was created using QGIS (QGIS Development Team, software version 3.16.13, https://www.qgis.org).

Figure 2

Number of reported symptomatic dengue virus infections in Belo Horizonte in 2019.

Figure 3

Relationship between the controls and the basic reproduction number. For $u_A$ and $u_F$, the range from 0 to 1 was considered as the percentage of additional control: the amount of larvicide applied in kilograms, and the amount of adulticide applied in liters, respectively. The blue region (on the right) indicates ordered pairs, $(u_A,u_F)$, where $R_0(u_A,u_F)<1$, while the red region (on the left) indicates ordered pairs $(u_A,u_F)$, where $R_0(u_A,u_F)>1$ and therefore there is an epidemic. The green dashed line indicates ordered pairs, $(u_A,u_F)$, where $R_0(u_A,u_F)=1$.

Figure 4

Example of descending control. The control application $u(t)=(u_A(t),u_{F_1}(t))$ is performed from time $t_0=(t_A,t_{F_1})$ until time $t_0+\tau$, with $\tau =({\tau }_A,{\tau }_{F_1})$.

Figure 5

Example of step size control. The control application $u(t)=u_{F_2}(t)$ is performed from time $t_0=t_{F_2}$ until time $t_0+\tau$, with $\tau ={\tau }_{F_2}$.

Figure 6

Curve fitting of the symptomatic infected population (I) from Belo Horizonte.

Figure 7

Populations evolution after model fitting for the year 2019.

Figure 8

Nondominated front in the objectives space $J_1$ (the control costs) $\times J_2$ (the hospital costs). The figure on the right side (b) is a zoom of the knee region of the figure on the left side (a), selected in red.

Figure 9

Different percentages of larvicide and adulticide and their associated decrease in hospital costs, increase in vector control costs, and changes in total costs for the selected nondominated front points.

Figure 10

Mosquito populations evolution after point C additional control measure implementation. The vertical lines represent the implementation start dates for each additional control cycle.

Figure 11

Evolution of the threshold $R_0$ without and with additional control actions considering the measures defined in point C.