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QUALITATIVE STUDY FOR A MULTI-DRUG RESISTANT TB MODEL WITH exogenous reinfection AND RELAPSE

International Journal of Biomathematics 2012年第4期5卷 157-175页

作者： LUJU LIU XINCHUN GAO School of Mathematics and Statistics Henan University of Science and Technology Luoyang 471003 P. R. China School of Basic Studies SIAS International College Zhengzhou University Zhengzhou 451150 P. R. China

One tuberculosis transmission model is formulated by incorporating exogenous reinfec- tion, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.

关键词： exogenous reinfection relapse the effective reproduction number the invasion reproduction number center manifold theory stability.

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Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB:An optimal control application

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Infectious Disease Modelling 2023年第2期8卷 574-602页

作者： Zenebe Shiferaw Kifle Legesse Lemecha Obsu Department of Mathematics Adama Science and Technology UniversityAdamaEthiopia

COVID-19 and Tuberculosis(TB)are among the major global public health problems and diseases with major socioeconomic *** dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be *** this study,we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and *** conditions are derived for the stability of both COVID-19 and TB sub-models *** certain conditions,the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than *** equilibria of the full TBCOVID-19 model are locally asymptotically stable,but not globally,due to the possible occurrence of backward *** incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R_(0)exogenous reinfection rate greater than a threshold(η>η*).The analytical results show that reducing R_(0)<1 may not be sufficient to eliminate the disease from the *** optimal control strategies were proposed to minimize the disease burden and related *** existence of optimal controls and their characterization are established using Pontryagin's Minimum ***,different numerical simulations of the control induced model are carried out to observe the effects of the control *** reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

关键词： COVID-19 Co-infection exogenous reinfection Basic reproduction number Bifurcation Optimal control

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