Study On The Effect Of Low Dose Drug Treatment On The Drug Resistance Of Malaria

Infectious diseases are widespread in people’s daily life and seriously affect people’s lives. Malaria is similar to most infectious diseases and is mixed in the human body. In this paper, we establish the epidemic dynamics model of the interaction between healthy red blood cells, resistant Plasmodium and sensitive Plasmodium in mixed infection state. In order to study the changes in the number of the common competitive resources of the resistant and susceptible parasites, and the effect of a small amount of the drug on the evolution of the malaria parasite.The dynamic properties of the model are analyzed. Firstly, The basic reproduction number is calculated, and the existence conditions of the disease free equilibrium,boundary equilibrium and endemic equilibrium of the model are presented. Secondly,the stability and bifurcation of equilibrium points in different conditions are analyzed.The local and global asymptotic stability conditions of disease-free equilibrium and the local asymptotic stability conditions of the boundary equilibrium points are obtained by using the LaSalle invariant principle and the Hurwitz criterion. At the same time, it is proved that the stability of the positive equilibrium is not stable. The existence of the super critical bifurcation of the fixed point of the system is proved by the central popular theorem and the standard type method. Finally, the numerical simulation is used to verify the validity of the results and discuss the effect of low dose of the drug on the existence and stability of the equilibrium point. Theoretical analysis and numerical calculation show that when the host appeared mixed Plasmodium infection state, along with the change of time and applied dose, only one type of parasite exist in the host and phenomenon of coexistence of drug-resistant Plasmodium and sensitive Plasmodium does not happen.