Assessing mosquito dynamics and dengue transmission in Foz do Iguaçu, Brazil through an enhanced temperature-dependent mathematical model

Abstract

Dengue fever remains a major public health concern, requiring continuous efforts to mitigate its impact. This study investigates the influence of key temperature-dependent parameters on dengue transmission dynamics in Foz do Iguaçu, a tri-border municipality in southern Brazil, using a mathematical model based on a system of ordinary differential equations. The fitted model aligns well with observed data. To track changes in dengue transmission over time and detect epidemic onset, we calculated the effective reproduction number. Additionally, we explored the potential effects of climate variability on dengue dynamics. Our findings highlight the importance of vector population dynamics, climate, and incidence, offering insights into dengue transmission in Foz do Iguaçu. This research provides a foundation for optimizing intervention strategies in other cities, improving outbreak prediction, and supporting public health efforts in dengue control.

Fig 1. Complete model diagram.

Schematic representation of the model proposed by [26], and further refined in this study. The diagram illustrates the population compartments and their transition rates, with arrows indicating the direction of population flow. Dashed lines highlight interactions between the mosquito and human populations.

Fig 2. Functional form of parameters b(T(t)), βm(T(t)), and βh(T(t)).

The temperature dependence of these parameters is modeled using the Brière function (Eq 5), fitted to dengue case data. The fitted coefficients are: $a_b=5.0366·{10}^{-4}$, $a_m=6.5093·{10}^{-4}$, and $a_h=1.0546·{10}^{-3}$.

Fig 3. Foz do Iguaçu datasets.

Panel showing the datasets used in this study: a) Time series of dengue cases in Foz do Iguacu, Brazil, from 2010 to 2022. The shaded green area highlights the periods used for curve fitting. The inset compares the number of trapped mosquitoes and dengue cases from 2017 to 2022. (b) and (c) Time series of bimonthly trapped mosquitoes alongside temperature and precipitation, respectively. Both are smoothed with moving averages (two-week for temperature and three-week for precipitation) over the period with available mosquito data.

Fig 4. Serotype data for epidemic years.

Description of the predominant DENV serotypes between 2010 and 2020 in Foz do Iguaçu, Brazil. It shows that DENV-1 was prevalent between 2010 and 2016 while we observed a strong detection of DENV-2 in 2020.

Fig 5. Mosquito model sensitivity analysis.

Sobol’ sensitivity analysis evaluating the importance of selected parameters in the mosquito populational model, concerning the total number of trapped mosquitoes simulated. Here S1 and ST represent first-order and total sensitivity indices, respectively. The analyzed parameters and their corresponding scanned intervals were: δ: [0,9]day⁻¹, ${\gamma }_m$: [0, 0.2]day⁻¹, ${\mu }_a$: [0.0234,0.5]day⁻¹, ${\mu }_m$: [0.0301, 0.109]day⁻¹, C₀: [10, 100], 𝜖: [0, 1000], b_cap: [0.001, 1.2].

Fig 6. Mosquito populational model fitting.

Bimonthly data of trapped mosquitoes and simulated curve of the mosquito model with the following fitted parameter values: $C_0=1.27·{10}^5,b_{cap}=0.3165,ϵ=909$ days.

Fig 7. Complete model sensitivity analysis.

Sobol’ sensitivity analysis evaluating the importance of selected parameters in the dengue transmission model, concerning the total number of infected humans simulated. Here S1 and ST represent first order and total sensitivity indices, respectively. The analyzed parameters and their corresponding scanned intervals were: a_b:[0.0007,0.00138], $a_{{\beta }_m}:[0.0007,0.00138]$, $a_{{\beta }_h}:[0.0007,0.00138]$, C₀:[12, 28], ${\alpha }_h:[0.083,0.25]da{y}^{-1}$, ${\theta }_h:[1/12,1/3]da{y}^{-1}$.

Fig 8. Dengue transmission model fittings.

Comparison between observed and simulated weekly dengue cases. The black line represents notified dengue cases, while the orange line shows the simulated cases from the dengue transmission model with the following fitted parameter values for the outbreaks of 2015-2016 (a): $\varphi =0.075$, $a_b=5.316\times {10}^{-4}$, $a_m=6.616\times {10}^{-4}$, $a_h=1.06\times {10}^{-3}$, with constant carrying capacity C₀ = 0.999. For the outbreak of 2019-2020 (b), we have: $\varphi =0.14$, $a_b=5.22\times {10}^{-4}$, $a_m=4.203\times {10}^{-4}$, $a_h=1.05\times {10}^{-3}$, with constant carrying capacity C₀ = 1.33.

Fig 9. Basic reproductive number estimation through data.

Graphical representation of the R₀ estimation method based on dengue cases data. The black lines show the number of new cases plotted against the cumulative number of cases. The red dashed lines indicate the end of the linear phase, marking the point where the initial exponential growth approximation is no longer valid. The red solid lines represent the fitted curve used to estimate R₀. Panel (a) corresponds to data from the 2010 dengue epidemic, while panel (b) shows data from 2020.

Fig 10. Effective reproduction number and temperature influence on dengue transmission.

Time series showing the relationship between the effective reproduction number R(t), temperature, and reported dengue cases. The red line represents R(T(t)) varying dynamically with temperature, while the black line shows $R(T={21.9}^{\circ }C)$ calculated with parameters in the mean daily temperature for Foz do Iguaçu. The orange line corresponds to the temperature time series, and the purple line represents the notified dengue cases data. Each parameter used is present in Table 1 and is multiplied by seven for weekly values.