Abstract
A spatiotemporal epidemic model with nonlinear incidence rate and Neumann boundary conditions is investigated. On the basis of the analysis of eigenvalues of the eigenpolynomial, we derive the conditions of the existence of Hopf bifurcation in one dimension space. By utilizing the normal form theory and the center manifold theorem of partial functional differential equations (PFDs), the properties of bifurcating periodic solutions are analyzed. Moreover, according to numerical simulations, it is found that the periodic solutions can emerge in delayed epidemic model with spatial diffusion, which is consistent with our theoretical results. The obtained results may provide a new viewpoint for the recurrent outbreak of disease.
Highlights
New infectious diseases continuously emerge, and existing diseases recurrently outbreak [1,2,3,4,5,6,7,8,9]
The numerical results validate our theoretical findings, which show that the length of the incubation period have significant impacts on epidemic transmission
The biennial outbreaks of measles is the signature of an endemic infectious disease, which becomes non-endemic if there were a minor increase in infectivity or a decrease in the length of the incubation period [15]
Summary
New infectious diseases continuously emerge, and existing diseases recurrently outbreak [1,2,3,4,5,6,7,8,9]. Ebola virus was firstly discovered in 1976, which began to outbreak in Guinea in February 2014, spread to West Africa. It caused serious death and social panic. In order to provide some suggestions for the prevention and control of the disease, it is necessary to establish rational mathematics model based on infectious mechanism of disease, the route of transmission, and the symptoms of the infected individuals. The incidence rate describes the number of new infections per unit time, which largely reflects the transmission mechanism of the disease [13,14,15,16,17]. Some reasonable suggestions can be provided for the prevention and effective control of infectious diseases
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