INTRODUCTION Dengue is a disease caused by any one of five virus serotypes and transmitted to humans by the Aedes aegypti mosquito. Climate change and health conditions have combined to make dengue a global public health problem. The situation is especially serious in Colombia, where by week 36 of 2018, dengue incidence was 96 cases per 100,000 population, with a total of 111 deaths. Different mathematical and statistical models have been proposed to understand the dynamics of transmission and consequently to apply control strategies to reduce the number of dengue cases.

OBJECTIVE Forecast the number of dengue cases expected in Colombia from 2018 through 2022 with the stochastic Auto-Regressive Integrated Moving Average (ARIMA) model and use the results to adjust the parameters of an ordinary differential equations model in order to determine the disease’s basic reproduction number in the year presenting the highest number of dengue cases.

METHODS An ecological time series study was conducted to forecast dengue incidence in Colombia from 2018 through 2022. The data were compiled from Colombia’s National Health Institute series on dengue cases reported by epidemiological week from 2009 to 2017. The stochastic ARIMA time series model was applied. Forecasts were then analyzed, and the year with the highest number of predicted cases was used to adjust the parameters of an ordinary differential equations model (ODE) through nonlinear least squares regression to calculate the vectorial capacity of the transmitting mosquito.

RESULTS Forecasts of the total number of dengue cases per year in Colombia for the following five years were: 32,411 (2018); 88,221 (2019); 56,392 (2020); 47,940 (2021); and 77,344 (2022). The highest number of cases was forecast for 2019. Values for the parameters affecting dengue transmission that year (by the year’s four quarters), such as recovery rate (0.0992, 0.0838, 0.1177, and 0.1535, respectively), vectorial capacity of the transmitting mosquito (0.1720, 0.1705, 0.1204, and 0.2147, respectively) and the basic dengue reproduction number (1.73, 2.03, 1.02, and 1.40, respectively) were estimated, indicating that most cases would occur in the second quarter and, since the basic reproduction number values were >1, the disease would persist in the country throughout the entire year.

CONCLUSIONS ARIMA model forecasts for 2018 through 2022 predicted the highest incidence of dengue cases in Colombia would occur in 2019. Comparison of ARIMA model forecasts and the ODE model allowed projections of possible variations in dengue cases reported, and the basic reproduction number predicted that dengue would persist throughout 2019.

KEYWORDS Arboviruses, climate, dengue, models, theoretical, basic reproduction number, prognosis, Colombia