| Zika is an arbovirus transmitted primarily by mosquitoes,which poses a great threat to the life and health of newborns.From its discovery to outbreak,many scholars have conducted a lot of research on the transmission mode and dynamics of Zika virus.On this basis,this paper establishes the transmission model of Zika virus with multiple transmission modes,analyzes its stability and studies its optimal control.The parameters in the model are reasonably estimated based on the actual data of Zika cases in Colombia.By comparing the influence of different control measures on the number of different patients,the corresponding optimal control strategy is obtained.In Chapter 1,the background knowledge about Zika virus and research status are introduced and the preparatory knowledge is described.In Chapter 2,the establishment of a new model of transmission of Zika virus through mosquito bites to humans,male-female contact and vertical transmission.Among them,sexual transmission distinguishes between men and women,and the virus is generally transmitted from men to women.Vertical transmission is divided into two types,one is human vertical transmission,and the other is mosquito vertical transmission.The vertical transmission of the virus in humans is the risk of microcephaly in babies born to women infected with Zika during pregnancy.Vertical transmission of mosquitoes means that infected females are more likely to transmit the virus to their offspring and lay eggs that also carry Zika.In this paper,the basic regeneration number R0 is calculated by using the next generation matrix method.Meanwhile,the local stability and global stability of the disease-free equilibrium point are proved.Then,the existence of optimal control is analyzed and the mathematical expression of optimal control is derived by using Pontryagin maximum principle.Based on the actual cases of Zika virus infection in Colombia 2015-2017,the MCMC algorithm is used to estimate the unknown parameter values of the model.Discuss the reasons for the deviation between the actual infection cases and the simulated results.According to a report by the World Health Organization,the results are due to measures to contain the Zika virus.In addition,different strategies for controlling Zika virus are simulated and compared.The results indicate that a combination of mosquito-borne control strategies and human internal control strategies is one of the most effective ways to reduce the risk of contracting Zika virus.In Chapter 3,due to the unclear research on newborn Zika virus infected in the previous chapter,based on the model study in the second chapter,the expression form of Zika virus transmitted by sexual transmission is simplified and gender is not differentiated to represent Zika virus transmitted by sexual transmission.In vertical transmission mode,neonatal infected persons were classified as a single compartment to establish a new transmission model of Zika virus for study.The basic regeneration number is derived and its stability is analyzed.The existence of optimal control is studied and the expression of optimal control is derived.The piecewise data fitting is carried out with the MCMC algorithm combining with the actual cases and the unknown parameters of the model are estimated.Finally,by comparing control measures to delay pregnancy and increase treatment rate,it is concluded that increasing treatment rate is more effective in reducing the number of Zika infections. |
