Reduction of discrete‐time infectious disease models

In this work, we propose the construction of discrete-time systems with two time scales in which infectious diseases dynamics are involved. We deal general situations. first, consider that individuals affected by disease move between generalized sites on a faster scale than itself. The second situation includes acting together another slower process. Once models have been built, conditions established so analysis asymptotic behavior their solutions can be carried out through reduced models. This is done using known reduction results for scales. These applied new first them illustrates proposed situation, being local SIS-type disease. Conditions found eradication or global endemicity model, case co-infection primary and an opportunistic treated, latter former. proposed.