A Population Model with Periodic Delay

Abstract

The rhythm of life on earth, occurring on daily or annual scales, is driven by seasonal changes in the environment [348] which regulate various physiological and behavioral processes, as well as the population dynamics of species. Many plant and animal species have demonstrated seasonal population dynamics in response to seasonal environmental changes, in particular, the weather conditions. Mosquito species Culex pipiens and Culex restuans, main vectors of West Nile virus transmission, are very sensitive to long-term variations in climate and short-term variations in weather [397], in particular, temperature condition affects the rates of immature mosquito development and activity of adults, and precipitation determines the amount and quality of larval habitats. Temperature also affects the host-seeking activity of ticks and their rates from one life stage to the next one, as a result, it is proposed as a statistically significant determinant and possible driver of emergence of the tick in Canada [262]. Seasonal forcing in host and parasite biology also determines the risk of infectious diseases through the following aspects [10]: (a) host social behavior and aggregation; (b) vector population and activity; (c) parasite stages in the environment; (d) timing of reproduction and pulses of susceptible hosts; and (e) host susceptibility and immune defences.