@okebilion  here is the corrected system of equation

solve({sigma*E-(mu+alpha+gamma)*I = 0, gamma*E+Lambda*N*p-(mu+alpha)*R = 0, Beta__1*S*E+Beta__2*S*I/(I*M+1)-(mu+sigma)*E = 0, Lambda(1-p)*N-mu*S-Beta__1*S*E-Beta__2*S*I/(I*M+1) = 0}, {E, I, R, S})

@acer I declared imaginaryunit=IM. the equations was solve but not well factored. 

@acer sorry for my manner at which I upload the question. I am really greatful for your insight. It  was really helpful. Would appreciate more if New[4] is full simplified.