Persistence or disappearance dynamics of a vector-borne disease model with climate change and distributed delay

This paper is concerned with the dual influences of climate change and distributed delay on dynamics of a vector-borne disease model. Compared to the previous works, the effect of climate change in a latent infection model is first considered since it increases the viral transmission probability of cross species. To deal with the non-monotonicity and heterogeneity of the model, we use some new ideas to investigate the spatio-temporal dynamics. The theoretical analyses suggest that three scenarios will occur as follows (i) If the disease persistence ahead of the climate change, the disease will die out by limiting the propagation speed of susceptible or infected individuals. (ii) The emergence of pulse type epidemic wave is obtained, which means the disease switches rapidly between persistence and disappearance. (iii) If susceptible individuals track the speed of climate change while infected individuals do not, the disease cannot evolve to the endemic disease.