One of the problems associated with the pandemic caused by COVID-19 is the search of positive cases from suspected cases. Another problem is predicting potentially severe or fatal cases from positive COVID-19 cases. Data associated with transmissible disease cases such as COVID-19 can be structured in the form of contact and infection graphs. In this sense, this work proposes a computer system based on graphs for monitoring probable cases and prediction of critical cases of COVID-19. These massive records could be used by teams of epidemiologists responsible for health surveillance to identify profiles with a greater possibility of being positive or severe cases of COVID-19. Monitoring is based on contact graphs and prediction employing descriptive and predictive models from data provided by the General Directorate of Health Surveillance.