Spreading Speed for a Vector‐Borne Disease System on Non‐Coincident Straight Infinite Cylinders

ABSTRACT

Vector‐borne diseases remain an increasing global public health concern. In this work, we investigate the spreading speed of vector‐borne disease via a four‐component reaction–diffusion system posed on non‐coincident straight infinite cylinders, which stands for an unconventional spatial configuration. We first establish the existence and uniqueness of a global solution by using the integrated semigroup theory, then by using duality arguments and a local maximum principle, we show the boundedness of this solution. For the long time behavior of the solutions, we derive a criteria condition for whether the disease dies out or spreads, governed by the sign of a suitable elliptic principal eigenvalue. In the case where spreading occurs, we determine an associated spreading speed by constructing appropriate sub‐ and super‐solutions.