Effects of vector preferential settling in the dynamics of a plant virus model with latent periods

Insect vectors transmit many plant viruses of agricultural importance. In most cases, these viruses manipulate their vectors' behavior and movement leading to vector settling and feeding preferences that influence virus spread. The latent period within the insect vector is also crucial in virus transmission during vector feeding, however is assumed to be negligible in previous studies. This paper proposes a plant-virus model with a focus on vector settling preference for virus-infected plants and considers the latent periods in both the plant and insect vector populations by introducing them as time delays. We analyze the existence and local stability of the equilibrium solutions using the basic reproduction number of the proposed model which is inversely related to the saturation parameter due to vector preference. We investigate the effects of the time delays on the local stability of equilibria and the possible emergence of stable limit-cycle solutions. Moreover, our theoretical results are corroborated using numerical continuation and bifurcation analysis to provide more insights into how the latent periods and vector preference affect the system's dynamics. Particularly, we show numerically that increasing the saturation parameter due to preferential settling reduces the number of new infections, if not eradicates the infection in the system.