Study of the Equilibrium of Systems with Elements in Several States Applying Operators with Shift

In our latest research on systems with renewable resources, we moved on to studying systems with elements that can be in different states. The states differ significantly in their processes of mortality, reproduction, and mutual influence. For instance, infected elements can have a higher mortality rate than healthy and recovered ones. In this paper, we continue the study of this theme. We are still interested in cyclic systems, in which the initial state of the system coincides with the final state. New content in this study is the expansion of assumptions about processes in the sets of elements in the second state: in the set of infected, diseased elements. It leads us to new complications and difficulties related to balance relations and functional operators with shift. Linear functional three-term equations are considered, a solution of balance equations is found and the equilibrium state of the system is determined.