Abstract
This paper concerns with a reaction–diffusion susceptible-vaccinated-infectious-recovered model with a fixed latent period. The model is formulated as a non-local and time-delayed reaction–diffusion model due to the fact that an individual infected by the disease in one place may not stay at the same space in the domain due to the movement of human during the incubation period. We then derive the basic reproduction number as the spectral radius of the next infection operator and show that it serves as a threshold role in predicting whether the disease will spread. Further, the explicit formula of basic reproduction number is obtained when all model parameters to be positive constants and the domain to the one-dimensional case. Moreover, we demonstrate the differences in the form of basic reproduction number between the standard incidence and bilinear incidence rate.
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Acknowledgments
The authors would like to thank the anonymous referees and the editor for their helpful suggestions and comments which led to the improvement of our original manuscript. The authors would like to thank the editors and the referees for their helpful comments.
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Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.