Impulsive delay equation models for the control of vector-borne diseases
Stephen Gourley (University of Surrey)
Thursday 21st January, 2010 14:00-15:00 326, Maths Department
Delay equation models for the control of a vector-borne disease such as West Nile virus will be presented. The models make it possible to compare the effectiveness of larvicides and adulticides in controlling mosquito populations. The models take the form of autonomous delay differential equations with impulses (if the adult insects are culled) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where the insect larvae are culled). Sufficient conditions can be derived which ensure eradication of the disease. Eradication of vector-borne diseases is possible by culling the vector at either the immature or the mature phase. Very infrequent culling can actually lead to the mean insect population being increased rather than decreased.