On a modification of a discrete epidemic model

In this paper under some conditions on the constants A; B 2 .0;1/ we study the existence of positive solutions, the existence of a unique nonnegative equilibrium and the conver- gence of the positive solutions to the nonnegative equilibrium of the system of difference equations xnC1 D .1 􀀀 yn 􀀀 yn􀀀1/.1 􀀀 e􀀀Ayn /; ynC1 D .1 􀀀 xn 􀀀 xn􀀀1/.1 􀀀 e􀀀Bxn / where A; B 2 .0;1/ and the initial values x􀀀1; x0; y􀀀1; y0 are positive numbers which sat- isfy the relations x0Cx􀀀1 < 1; y0Cy􀀀1 < 1; 1􀀀y0 > .1􀀀x0􀀀x􀀀1/.1􀀀e􀀀Bx0 /; 1􀀀x0 > .1 􀀀 y0 􀀀 y􀀀1/.1 􀀀 e􀀀Ay0 /.