Dynamics Modeling And Rabies Prevention And Control Measures To Study In China

Rabies, also called Hydrophobia or Mad Canine Disease, is an acute anthropozoonosis ofthe nervous system caused by rabies virus. Clinical features mainly are afraid of water, pho-tophobia, dysphagia, mania and so on. Once symptoms of the disease develop, its mortalityreaches up to 100%. The number of deaths in China due to rabies is only second to India.After 1950s in China, there appear three peaks. In China, the main source of human rabiesis dog. Within the perspective of the time distribution of rabies case, rabies can be infectedall years. However, after 2003, the seasonality of cases is more obvious, mainly focusing onautumn (July-September) and winter (October-December). Within the perspective of theregional distribution of human infected cases, the rabies outbreak mainly distributes thesouth, southwest and east of China, and appears the difusion from the south to the north.However, nowadays few literature makes use of the dynamical model to study the rabies inChina. In order to explore efective control and prevention measures, this paper makes thefollowing researches.1. Considering that the main source of human rabies in China is dog, we build anSEIRS coupled dynamical model including the populations of human and dog to describethe spread of rabies among dogs and from dogs to humans. Besides analyzing the dynamicalbehavior, combining with the human rabies data reported by the Chinese Ministry of Health,this paper takes the model to simulate the data and predict that the number of the humanrabies. Lastly, this paper performs some sensitivity analysis of R0in terms of the modelparameters. By analysis, it comes to a conclusion: the basic reproduction number R0= 2for the rabies transmission in China. It can be predicted that the number of the humanrabies may reach another peak around 2030. Combining controlling the birth number withenhancing the vaccination coverage rate of dogs is the efective measure to control rabies.2. Considering the seasonality of rabies cases, this paper proposes an SEIRS nonau-tonomous dynamical model with periodic transmission rates to investigate the seasonal rabiesepidemics. With regards to the periodic model, the paper evaluates the basic reproduction number and analyzes the dynamical behavior of the model. Moreover, this paper takes themodel solution to simulate the monthly data of human rabies cases reported by the ChineseMinistry of Health. Lastly, we also carry out some sensitivity analysis of the basic reproduc-tion number R0in terms of relevant model parameters and assess the prevention and controlmeasures under periodic model. By above analysis, it come to a conclusion that it is morereasonable to regard R0as a threshold for the disease rather than the average basic repro-duction numberRˉ0or the basic reproduction numberR 0of the corresponding autonomoussystem. Besides controlling the number of dogs, reducing the birth rate of dogs, increasingthe immunization rate of dogs, enhancing the management of dogs, people should enhancethe supervision for pupils and children before the peak of rabies comes per year.3. Considering the difusion of rabies in China, this paper constructs an SEIRS dy-namical reaction-difusion model to study how the movement of dogs leads to and impactsthe spatial spread of rabies. According to the reaction-difusion model, besides obtainingthe minimal wave speed, this paper discusses the local stability of the endemic equilibriumtheoretically. Moreover, resorting to the numerical method, the paper proves the existenceof traveling waves and the infuences of parameters on human rabies cases and the minimalwave speed. Through above researches, it can be obtained that with regards to the reaction-difusion model, the positive equilibrium still be stable, that is, the spatial pattern cannotappear. The movement of dogs not only leads to the emerging of travelling wave, but alsoarouses the difusion of human rabies. The movement speed of the incubative and infectiousdogs has the largest infuence on the minimal wave speed, so the government should enhancethe management for dogs to prevent the difusion of rabies. If in order to eliminate rabiesthoroughly, it needs other prevention and control measures such as vaccination.