LYAPUNOV'S STABILITY ON SOLUTION OF A CLASS OF SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS AND APPLICATION IN POPULATION CONTROL WITH ILLNESS

In this paper, we will discuss a class of integro-differential system of equations. It is a mathematicalmodel which is drown from the practical problems of the population control system with illness:where 0 【r’ m【rm and rm is the highest age over attained by individual of the population. In this pa-per, P1= P1（x,t） denotes the age density function of the healthy population; P2 = P2（r,s,ts） denotes theage and period of illness density function of the morbid population; λ（r） =λ（r,t） denotes the relative inci-dence of diseases; η（r,s） =η（r.s.t）denotes the relative recovering rate of patients;μ2（r,s） = μ2（r,s,t）denotes the relative mortality of patients. And the other functions μ1,（r） =μ1,（r,t）, β=β（t） , h（r）