Modeling the Dynamic of Multi-Wave Diseases: The Model of Hand, Foot and Mouth Disease

An HFMD outbreak spread over the city of Hải Phòng from Summer 2011 to Autumn 2012. This epidemic was chosen because it was the very first HFMD epidemic in North Vietnam, eliminating thus interferences with previous outbreaks. This epidemic displayed 3 separate waves. A complete dataset was collected for more than 9500 patients during this period, which enabled us to analyze this epidemic at different scales. Access to the healthcare system was crucial during this period, with a reorganization of the system in February-March 2012. An analysis at commune level enables us to track the epidemic along certain communication routes. The three-waves structure reveals a wide disparity at district level. We develop a mathematical model showing high accuracy at the adjustment of data for both the total number of cases and for the number of cases per week. As a consequence, the model was able to accurately determine the dates of beginning and end of each wave and to show that they overlapped. Using mathematical functions associated with this model, it was possible to calculate the probability for a patient to belong to a specific wave.