Integral equations for the force of infection were derived taking into account spatial variables.
Those equations were studied both numerically and with functional analysis techniques.
Threshold conditions for the establishment of the infection were also derived.
The existence of travelling waves of the infection was investigated.
An integral equation for the shape of the wave front was deduced.
Conditions for the existence of those waves were derived independently of the velocity of propagation.
The model differs from previous studies in that we allow recovery from the infectious status and/or demographic structure in the host population, that is, deaths and births of individuals.
Mots-clés Pascal : Epidémiologie, Modélisation, Infection, Loi action masse, Equation différentielle, Equation intégrale, Opérateur intégral, Calcul opérationnel, Solution numérique, Bifurcation, Espace Banach, Existence solution, Unicité solution, Opérateur linéaire, Méthode Gauss, Onde épidemie, Opérateur Volterra, Opérateur Hammerstein, Dérivée Fréchet
Mots-clés Pascal anglais : Epidemiology, Modeling, Infection, Mass action law, Differential equation, Integral equation, Integral operator, Operational calculus, Numerical solution, Bifurcation, Banach space, Existence of solution, Solution uniqueness, Linear operator, Gauss method, Epidemic wave, Volterra operator, Hammerstein operateur, Fréchet derivative
Notice produite par :
Inist-CNRS - Institut de l'Information Scientifique et Technique
Cote : 99-0478225
Code Inist : 001A02E07. Création : 22/03/2000.