Investigating the seasonality of disease incidences is very important in disease surveillance in regions with periodical climatic patterns. In lieu of the paradigm about disease incidences varying seasonally in line with meteorology, this work seeks to determine how well simple epidemic models can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the disease occurrences can be performed using the classical Floquet theory, which explains the stability of the existing periodic solutions. For an illustrative case, we employed infected-recovered models with an infection rate of a single period and that of commensurate periods to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered version. To estimate the infection rate of a single period, eight optimization schemes were assigned returning magnitudes of the rate that vary insignificantly across schemes. Three schemes were assigned to estimate the infection rate of commensurate periods based on three different sets of periods used. Each scheme involving commensurate periods gives better fitting than that involving only a single period. The computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.
- Basic reproductive number
- Data assimilation
- Floquet theory
- Infected-recovered model
- Nonautonomous periodic system