Spatial-temporal risk index and transmission of a nonlocal dengue model. (June 2020)

• Record Type: Journal Article
• Authors: Zhu, Min; Lin, Zhigui; Zhang, Lai
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: Dengue model -- Basic reproduction number -- Nonlocal incidence -- Free boundaries; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103076
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The nonlocal incidence and free boundaries are introduced into a classic SIR-SI model describing the transmission dynamics of dengue fever, where the nonlocal incidence allows for interactions of susceptible population at a given location with infected mosquitoes in the whole area, and free boundaries represent the expanding front of the area contaminated by dengue virus. We derive a spatial–temporal risk index in terms of the basic reproduction number, which depends on the nonlocal incidence and time variable. More importantly, we explore the relationships between different model variants regarding these risk indices. We additionally find sufficient conditions to ensure the vanishing and spreading of dengue fever, and demonstrate, for a special case, the asymptotic behavior of its solution when spreading occurs. Finally, we carry out numerical simulations to demonstrate our analytical findings and further provide their epidemiological explanations.