Lubuma, Jean M.-S.Terefe, Yibeltal Adane2015-12-042015-09Lubuma, JM-S & Terefe, YA 2015, 'A nonstandard Volterra difference equation for the SIS epidemiological model', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A : Matematicas, vol. 109, no.2, pp. 597-602.1578-7303 (print)1579-1505 (online10.1007/s13398-014-0203-5http://hdl.handle.net/2263/51056By considering the contact rate as a function of infective individuals and by using a general distribution of the infective period, the SIS-model extends to a Volterra integral equation that exhibits complex behaviour such as the backward bifurcation phenomenon.We design a nonstandard finite difference (NSFD) scheme, which is reliable in replicating this complex dynamics. It is shown that the NSFD scheme has no spurious fixed-points compared to the equilibria of the continuous model. Furthermore, there exist two threshold parameters Rc 0 andRm0 , Rc 0 ≤ 1 ≤ Rm0 , such that the disease-free fixed-point is globally asymptotically stable (GAS) for R0, the basic reproduction number, less than Rc 0 and unstable for R0 > 1, while it is locally asymptotically stable (LAS) and coexists with a LAS endemic fixed-point forRc 0 < R0 < 1. A unique GAS endemic fixed-point exists whenR0 > Rm0 andRm0 < ∞. Numerical experiments that support the theory are provided.en© Springer-Verlag Italia 2014. The original publication is available at : http://link.springer.comjournal/13398.SIS modelVolterra integral equationDynamics preserving schemeNonstandard finite difference (NSFD) schemePostprint Article