Establishment And Analysis Of Infectious Disease Model Considering Control Strategy And Medical Resources

Infectious diseases has always been one of the most serious social problems. In order to control disease spread and hopefully eliminate epidemic disease, the government takes some intervention strategies, such as isolation, reporting news about the emerging diseases,mask wearing, vaccinating. On the other hand, the government provides relevant medical resources such as medical sta?, hospital bed, medical equipment. Mathematical models have been contributed to improve our understanding of infectious disease dynamics and helped us develop preventive measures to control infection spread qualitatively. In order to ?nd out the in?uence of intervention strategies on controlling disease, we make some researches:1.Cosindering the intervention strategies, we establish and study an SIR model with a saturated incidence rate and a nonlinear recovery rate de?ned as a function of the number of beds. We ?nd that the model undergoes a sequence of bifurcations including Saddle-Node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation. Then, we obtain that taking some intervention strategies at the initial moment of an emerging disease occur and providing enough medical resources are important for controlling endemic from these result.2.An SEIS model with latency and nonlinear recovery rate is investigated and analyzed.For the model, we ?nd that the basic reproduction number R0 is no longer a threshold parameter. When R0< 1, there may exists two endemic equilibrium for the model. Furthermore,we obtain the condition under which the system undergoes backward bifurcation. From the result, we know that the infection will spread qualitatively if the number of hospital bed is less than a certain critical value. Therefore, it is conducive to control the disease when we increase the input number of hospital beds.3.In the real life, vaccination is one of the most e?cient interventions. Hence, we establish and study an SVIS model with vaccination and a recovery rate de?ned as a function of the number of the beds. For the model, we ?nd that the reproduction number R0 is the function of the vaccination rate φ and is no longer a threshold parameter. There exist an unique epidemic equilibrium when R0> 1, and may exist two epidemic equilibria or none when R0< 1. If there exist two equilibria, then the lower epidemic equilibrium is a hyperbolic saddle, and the higher epidemic equilibrium is an anti-saddle. Furthermore,we ?nd that the system undergoes backward bifurcation if the incidence rate is big or the number of beds is small. Hence, the infectious disease can be eliminated by increasing the number of beds or decreasing incidence rate when R0< 1.