Diffusion epidemic models with incubation and crisscross dynamics

Lyapunov functions and global stability for a spatially diffusive SIR epidemic model

“…Webb [13, Section 3] and Fitzgibbon et al [7,Section 4]) that A I is the infinitesimal generator of strongly continuous semigroup e tA I t≥0 in X. Then,…”

“…However, for space-structured epidemic models as reaction-diffusion equations, such a construction method has not been sufficiently established and the global stability results are restricted to some special cases that the coefficients are constant (see, for instance, Capone et al [3], Chinviriyasit and Chinviriyasit [4], Fitzgibbon et al [7], Lotfi et al [24], Melkemi et al [12], and Webb [13]). For diffusive epidemic models, the existence of traveling wave solutions has attracted sustained attention of researchers and has been one of the most interesting topics (see, for instance, Ducrot [5], Ducrot and Magal [6], Hosono and Ilyas [8], and Zhang and Wang [14]).…”

“…In particular, as spatially heterogeneous epidemic models, reaction-diffusion equations have been widely studied by many authors. We refer the reader to [2][3][4][5][6][7][8][9][10][11][12][13][14] and the references cited therein.…”

Galerkin methods for a model of population dynamics with nonlinear diffusion

“…1)-( 1.5) and compute the age-initial value ( 1.2) with appropriate numerical quadratures, which allow us to obtain a linear scheme. It is noted that our ideas can be applied to the related problems such as two-sex population models, S-I-R models, and various other epidemic models with spatial diffusion (see, for example, [ 5 ] and the references cited therein).…”

Spatiotemporal Transmission Dynamics of Recent Ebola Outbreak in Sierra Leone, West Africa: Impact of Control Measures

“…18 Under this assumption, diffusion is approximated by adding Laplacian diffusion terms to the ODEs that model the temporal dynamics. [19][20][21] The spread of disease is mainly characterized by local contacts between individuals, and therefore, the diffusion-type models are applied. Mathematical models of disease outbreaks can be helpful by providing forecasts about the development of the epidemic and by projecting the likely impact of proposed interventions before they are implemented.…”