Establishment And Analysis Of Infectious Disease Dynamics Model Based On Multiplex Networks

Infectious diseases have immeasurable harm to people's life and social development,and the research on various aspects of infectious diseases has been deepened.In this paper,two more reasonable dynamic model of infectious diseases are established on the multiplex network,and their transmission thresholds are analyzed.Chapter 1 introduces the necessity of infectious disease research and the research process of dynamic models of infectious diseases based on complex networks,then we give the main works of this paper.In Chapter 2,according to the transmission mechanism of the infectious diseases,we establish the dynamic model of infectious diseases based on the multiplex network(?)where(?)and(?).According to matrix theory and eigenvalue theory,we derive the the expression of transmission thresholds in two networks,and by using perturbation analysis prove that multiplex network transmission threshold is less than isolated network transmission threshold.At last,the corresponding numerical simulation results are consistent with the above conclusion.From this we can see that the mutual transmission between the two networks promotes the spread of diseases.In Chapter 3,based on the spread of different diseases in the same population,node-based markov equations are established on the overlay network:(?),where(?),and(?).According to matrix theory and eigenvalue theory,the transmission thresholds of the two diseases are obtained,Although the transmission of one disease affects the transmission rate of some individuals to another disease,it does not affect the transmission threshold of another disease.Finally the rationality of the results in this section is verified by the corresponding numerical simulation.In Chapter 4,we summarize the main conclusions of this paper and give some ideas for future research.