Abstract
We propose a numerical method for a general integro-differential system
of equations which includes a number of age-of-infection epidemic models in
the literature [1, 2]. The numerical solution is obtained by a non-standard
discretization of the nonlinear terms in the system, and agrees with the analytical
solution in many important qualitative aspects. Both the behaviour
at finite time and the asymptotic properties of the solution are preserved for
any value of the discretization parameter. These properties, together with
the fact that the method is linearly implicit, actually make it a computationally
attractive tool and, at the same time, a stand-alone discrete model
describing the evolution of an epidemic [3, 4].
References
[1] F. Brauer. Age of infection in epidemiology models, Electronic Journal of
Differential Equations, 2005.
[2] D. Breda, O. Diekmann, W. F. de Graaf, A. Pugliese and R. Vermiglio,
On the formulation of epidemic models (an appraisal of Kermack and McKendrick),
J. of Biological Dynamics, 6:sup2, 103-117, 2012.
[3] E. Messina, M. Pezzella and A. Vecchio, A non-standard numerical scheme
for an age-of-infection epidemic model, J. Comput. Dyn., 9 (2), 239-252, 2022.
[4] E. Messina, C. Panico and A. Vecchio, Global stability properties of nonstandard
discretization for renewal epidemic models, in preparation.
Anno
2023
Autori IAC
Tipo pubblicazione
Altri Autori
B.Buonomo, E. Messina, C.Panico, A.Vecchio