A Kind Of Host-Vector Transmission Dynamic Model And Optimal Control

The Host-Vector epidemic is an infectious disease induced by pathogene and spread by biological carrier.It threatens the health of human beings as an important branch of infectious disease.According to realistic situation and biological significance,mathematical models are formulated in order to investigate the transmission mechanics and laws,and further to find some feasible control strategies,which has been seen as a significant research field of mathematical epidemiology.The transmission characteristics of Host-Vector epidemic are different due to various patho-genes and biological carriers.Thus there exist a vast variety of mathematical models.In this paper,taking schistosomiasis as an example,we study a kind of Host-Vector epidemic with intermediate hosts.In consideration of multi-hosts problem,incubation period and uncertainty,diverse transmission dynamic models are constructed,and their stability behaviors are analyzed.Incorporating with the optimal control theory,some reasonable and effective control laws are suggested.The details of main work are proposed as follows.1.Mathematical model is used to do quantitative analyses of multi-hosts in the dynam-ics of schistosomiasis.We also incorporate bovines in the model to investigate their impact on transmission and controlling the spread of Schistosoma japonicum in humans in China.The theoretical results are rigorously proved for the local and global stabilities of the disease free equilibrium and the endemic equilibrium.The multi-host schistosomiasis optimal control problem is proposed by using optimal control theory.Theoretical analyses and numerical re-sults summarize some efficient control strategies for overcoming schistosomiasis:the infected bovines play an important role in the spread of schistosomiasis among humans,so killing the infected bovines will be useful to prevent transmission of schistosomiasis among humans;im-proving the treatment rate of infected humans,the killing rate of the infected bovines and the fishing rate of snails in the early stage of spread of schistosomiasis are very helpful to contain the prevalence of infected human case and minimize the total cost.2.A new mathematical model included an exposed compartment is established in con-sideration of incubation period of schistosoma in human body.The basic reproduction number is calculated to illustrate the threshold of disease outbreak.The existences of the disease free equilibrium and the endemic equilibrium are proved.Studies about stability behaviors of the model are exploited.Moreover,control measure assessments are investigated in terms of some special parameters in the basic reproduction number.Based on the results of control measure as-sessments,the corresponding optimal control problem according to the model is presented and solved.An effective control intervention for anti-schistosomiasis is sought out:decreasing the transmission rate from exposed humans to infected humans is reasonable method by enhancing the awareness and treatment proactivity of people.Finally,lots of numerical simulations are given to illustrate the rationality of the model and the validity of control laws.3.A compartmental dynamic model with time delays is established in order to investigate the effects of the incubations on schistosomiasis transmission.The threshold value of disease breakout is calculated.Two equilibrium points:a disease free equilibrium and an endemic e-quilibrium,are calculated respectively.The stability behaviors at the equilibriums are analysed by using the theory of delay differential equation.Some interesting results conquering schisto-somiasis are obtained from the point of view of time delay.(1)The incubation of egg hatching can postpone the outbreak of schistosomiasis.So it is an effective strategy for schistosomia-sis overcoming to prolong the incubation of egg hatching.(2)The time delays in miracidia and cercaria can make the disease spread lower.Thus lengthening the incubation periods in miracidia and cercaria do good to the prevention and control of schistosomiasis at the begin-ning.(3)The maturation periods of schistosome in human and sporocyst in snail could give rise to Hopf bifurcations and periodic orbits,respectively.The threshold value of disease breakout decreases with respect to the maturation of sporocyst.Therefore,it is a reasonable strategy for anti-schistosomiasis to prolong the maturation duration of sporocyst in snails.4.A schistosomiasis optimal control problem with uncertainty is studied.From the diffi-culty in realistic society,a common mathematical problem:a discrete-time nonlinear optimal control system with uncertain perturbation,is proposed.A value-iteration-based hybrid intelli-gent algorithm,incorporating heuristic dynamic programming algorithm and uncertain simula-tion,is presented.And some characters of the hybrid intelligent algorithm are provided.Two neural networks are used in the algorithm:a critic network is aimed at approximating the ob-jective function,as well as an active network is used to obtain an uncertain optimal control law.As an application,an uncertain schistosomiasis optimal control problem is solved to illustrate the feasibility and effectiveness of the hybrid intelligent algorithm finally.