TY - JOUR
T1 - Dynamics of a generalized nonlocal dispersion SIS epidemic model
AU - Djilali, Salih
AU - Bentout, Soufiane
AU - Tridane, Abdessamad
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
PY - 2024/12
Y1 - 2024/12
N2 - This paper explores a generalized nonlocal dispersion SIS epidemic model subject to the Neumann boundary conditions and spatial heterogeneity. We use a convolution operator to describe the nonlocal spatial movements of individuals. Our primary goal is to investigate this model, focusing on a generalized incidence function, which presents an additional challenge in the model analysis. This model’s basic reproduction number, R0, is identified, and it is proved that 1-R0 has the same sign as the principal eigenvalue of a generalized linear nonlocal operator. Furthermore, the asymptotic profiles of R0 in terms of dispersion coefficients are also established. We also investigate the existence and uniqueness of an endemic steady state for R0>1, and we study the large dispersal rates effect on the asymptotic profiles of the steady endemic state. Finally, we discussed the global asymptotic behavior of the solution for different dispersal coefficients.
AB - This paper explores a generalized nonlocal dispersion SIS epidemic model subject to the Neumann boundary conditions and spatial heterogeneity. We use a convolution operator to describe the nonlocal spatial movements of individuals. Our primary goal is to investigate this model, focusing on a generalized incidence function, which presents an additional challenge in the model analysis. This model’s basic reproduction number, R0, is identified, and it is proved that 1-R0 has the same sign as the principal eigenvalue of a generalized linear nonlocal operator. Furthermore, the asymptotic profiles of R0 in terms of dispersion coefficients are also established. We also investigate the existence and uniqueness of an endemic steady state for R0>1, and we study the large dispersal rates effect on the asymptotic profiles of the steady endemic state. Finally, we discussed the global asymptotic behavior of the solution for different dispersal coefficients.
KW - 35B40
KW - 45A05
KW - 45F05
KW - 92D30
KW - Neumann boundary conditions
KW - Nonlinear incidence function
KW - Nonlocal dispersion
KW - SIS model
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U2 - 10.1007/s00028-024-01013-1
DO - 10.1007/s00028-024-01013-1
M3 - Article
AN - SCOPUS:85205508245
SN - 1424-3199
VL - 24
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 4
M1 - 83
ER -