Dynamics of epidemics in homogeneous/heterogeneous populations and the spreading of multiple inter-related infectious diseases: Constant-sign periodic solutions for the discrete model

We consider the following model that describes the dynamics of epidemics in homogeneous/heterogeneous populations as well as the spreading of multiple inter-related infectious diseases:ui(k)=∑ℓ=k-τik-1gi(k,ℓ)fi(ℓ,u1(ℓ),u2(ℓ),…,un(ℓ)),k∈Z,1⩽i⩽n.Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic   solutions (u1,u2,…,un)(u1,u2,…,un), i.e., for each 1⩽i⩽n1⩽i⩽n, uiui is periodic and θiui⩾0θiui⩾0 where θi∈{1,-1}θi∈{1,-1} is fixed. Examples are also included to illustrate the results obtained.