Study On The Stability Of Two Types Of Nosocomial Antibiotic Resistance Models

In the first chapter of this paper,we demonstrate the grim situation of global antibiotic resistance,by studying the studies on antibiotic resistance from WHO since 2014 and the latest bacteria resistant test report from CARSS.We summarize two development trend of antibiotic resistance model research,by analysising the basic modeling idea and reasoning method of a series recent articles.Finally,we introduce the transmission mechanism,relative basic concepts,a modeling classification framework of antibiotic resistance.In the second chapter,we establish a nosocomial antibiotic resistance model with infection period delay,and consider both direct and indirect spread,in order to study the influence of infection period for spread.The probability of infected-patients is still in the hospital after the moment of t has been considered.We define the threshold of disease outbreak,obtain that if R₀<1,the disease-free equilibrium is globally and locally asymptotically stable for any ??0;if R₀>1,the endemic equilibrium of this model is exist and unique,it is globally and locally asymptotically stable for any ??0,by using Routh-Hurwitz criterion and LasalleLiapunov invariant set principle.Finally the numerical simulation verifies the correctness of the conclusion,analyses the influence of the length of infection time for the disease peak.In the third chapter,we set up an unidirectional antibiotic resistance propagation model with parameters of prevention and treatment function.By using Routh-Hurwitz criterion and the second additive composite matrix principle obtain that if R₀<1,the disease-free equilibrium is locally asymptotically stable;if R₀>1,the endemic equilibrium of the model is exist and unique,it is globally asymptotically stable.Finally a series of numerical simulations are given to illustrate the mathematical findings.