| The basic reproduction number, R0, is the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population. Most studies of epidemic models use the basic reproduction number as a threshold quantity for stability and control of diseases. But R 0 is usually calculated for autonomous systems at the disease free equilibrium using the next generation method. In a real life scenario, most species undergo seasonal eects and temperature dependencies. Further, the system might be in an endemic state when epidemiologists attempt a disease control strategy. These factors limit the usefulness of the basic reproduction number. In this thesis, we extend the notion of R 0 to a functional representation of state variables that can be used to evaluate the stability of the disease free solution of non-autonomous systems for any disease state. We demonstrate the equivalence between the new representation and R0 for autonomous systems and how the new representation can be utilized to nd the optimal parameter set for disease control methods. We also study several non-autonomous vector-host systems, obtain the dynamic threshold quantities for stability of the disease free state, and compare the dynamics with their autonomous analogs. |
