Research On Several Types Of Infectious Disease Models Affected By Disease Information Awareness

With the increasing maturity of the media technology,media coverage have been a non-negligible factor in the prevention and control of the spread of infectious diseases.In this paper,according to the study of systems both at home and abroad in recent years,In order to analyze the influence of awareness program on the spread of infectious diseases we construct two types of infectious disease model with awareness program.In chapter two,an epidemic model with segmented incidence rate was formulated and analyzed to describe the limit of media impact.We analyze the model by using stability theory of differential equations and reach the following conclusions: the disease-free equilibrium E⁰₁ is global asymptotic stable if and only if R₀ < 1;when 1 < R₀ < RIc,the endemic equilibrium E1* is global asymptotic stable;while when R₀ > RIc,the endemic equilibrium E2* is global asymptotic stable.Finally the numerical simulation shows that,if the critical value Ic is ignored,then the impact of information awareness program will be overestimated.In chapter three,Considering the time lag of information dissemination itself and media mechanism specified by Twitter,we proposed a mathematical model with time delay and the dynamics of “tweets”.The system exhibits three equilibria: when ? ? 0,the disease-free equilibrium E⁰₁ is stable if the basic reproduction number R₀ < 1 and the threshold Rc > 1;the disease-free equilibrium E⁰₁ is stable if R₀ < 1 and Rc < 1.The endemic equilibrium E* is stable when R₀ > 1 and 0 ? ? < ?₀,while a Hopf bifurcation can occur as delay increases when ? > ?₀.Numerical simulation validates the theoretical results we obtained and the increasing of the implementation rate can reduce the number of the infective population,and timely awareness program can reduce the outbreak of the disease.