The SEIRQ epidemic model can be described by the following system of ordinary differential equations(1) S′=p1(t)A(t)−βSI−σβSE−q1(t)S−B1,E′=p2(t)A(t)+βSI+σβSE−νE−q2(t)E−B2,I′=p3(t)A(t)+νE−q3I−αI−B3,R′=γ(t)Iq+αI+αIq,Sq′=q1(t)SEq′=q2(t)E−νEqIq′=q3I+νEq−γ(t)Iq−αIqwhere the prime (′) denotes the differentiation with respect to time t. Here, parameters 0 <  β, ν, γ(t), α  < 1 and the quarantined rates 0 ≤  q 1(t), q 2(t), q 3  ≤ 1. All the initial values of different individual groups: S(0), E(0), I(0), R(0), S q(0), E q(0), I q(0) are non-negative.