Research Projects

Dengue fever is a rapidly spreading vector-borne disease that affects a large number of people worldwide. It is caused by the dengue virus and transmitted by the Aedes aegypti mosquito. There is no specific treatment for dengue fever, and the prevention of the disease relies heavily on vector control strategies. Mathematical modeling has been used to study the transmission dynamics of dengue fever and to inform public health interventions. One approach to modeling dengue fever is to use fractional calculus, which extends the traditional calculus to include non-integer order derivatives. It allows for the modeling of systems that exhibit non-local and non-Markovian behaviors, i.e., behaviors that depend on the entire history of the system rather than just the current state. Traditional integer-order calculus is not well-suited to modeling such systems, but fractional calculus provides a framework to describe them it can also be used to model the effects of heterogeneity in a population. Traditional mathematical models of infectious diseases assume that the population is homogeneous, but in reality, individuals may differ in their susceptibility to infection, their contact patterns, and their response to interventions. Fractional calculus can help incorporate heterogeneity into the model and provide a more realistic representation of disease spread. The objective of this project is to develop a mathematical model for predicting dengue fever outbreaks and evaluating the effectiveness of various control strategies.