Modeling the uncertainty in epidemiological models through interval analysis considering actual data from two municipalities in Colombia affected by dengue

Abstract

Epidemiological models have become powerful tools for studying and understanding the characteristics and impact of transmitted diseases in a population. However, these models usually require specifying several values of input parameters obtained from experimental data, characterized by high uncertainty levels due to biological variation. This situation is evident for models that simulate the transmission of vector-borne diseases such as dengue, our case study. Therefore, treating and modeling this uncertainty is essential to ensure the robustness of designed models. For this, we propose to model the uncertainty through interval analysis by representing the input parameters and initial conditions by real closed intervals in the forward problem. This approach has the advantage of making a minimal number of assumptions concerning uncertainties, unlike the traditional methods (probabilistic and fuzzy). To illustrate the performance of this methodology, we consider a coupled ODE system of seven state variables and nine parameters, representing the transmission of Dengue between host-vector populations. Additionally, to enhance the use of the numerical method utilized for solving the system, the uncertain quantities (parameters and initial conditions) are determined based on the results of (i) the sensitivity analysis of R0, (ii) the structural identifiability analysis of the model, (iii) the characteristics of the available information about mosquito population, and (iv) dengue incidence data in two municipalities in Colombia, Itagüí and Neiva, during the outbreaks in 2016. We believe that the methodology proposed here to select and incorporate uncertainty in epidemiological models through interval analysis is widely applicable to other phenomena and models in science and engineering.