Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment

An SIR model for dengue disease transmission is discussed here. It is assumed that two viruses namely strain 1 and strain 2 cause the disease and long lasting immunity from infection caused by one virus may not be valid with respect to a secondary infection by the other virus. Our interest here is to derive and analyse the model taking into account the severe DHF compartment in the transmission model. The aim would be to find a control measure to reduce the DHF patients in the population, or to keep the number of patients at an ac- ceptable level. Analysis of this model reveals that there are four equilibria, one of them is the disease-free, the other three equilibria correspond to the presence of single serotype respectively, and the coexistence of two serotypes. Stability analysis of each equilibria and their relations with type reproductive numbers are shown. We also discuss the ratio between total number of severe DHF com- partment with respect to the total number of first infection compartment and the total number of secondary infection compartment, respectively. This ratio is needed for practical control measure in order to predict the “real” intensity of the endemic phenomena since only data of severe DHF compartment is available in the field.