The complete system in the transformed variables has the stable endemic equilibrium at the origin. To bound the dynamics to the first octant, we use the fact that s Ն 0, e Ն 0, and i Ն 0 to derive the appropriate inequalities for the transformed discrete variables u, v, and w. These inequalities can be found in Appendix C as Eq. ͑C1͒. These inequalities enable us to define new discrete variables Y 1 , Y 2 , and Y 3 given by Eqs. ͑C2a͒-͑C2c͒ in Appendix C.