COVID-19 and Tuberculosis(TB)are among the major global public health problems and diseases with major socioeconomic impacts.The dynamics of these diseases are spread throughout the world with clinical similarities wh...COVID-19 and Tuberculosis(TB)are among the major global public health problems and diseases with major socioeconomic impacts.The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated.In this study,we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB.Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria.Under certain conditions,the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one.The equilibria of the full TBCOVID-19 model are locally asymptotically stable,but not globally,due to the possible occurrence of backward bifurcation.The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R_(0)<1 and the 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 community.The optimal control strategies were proposed to minimize the disease burden and related costs.The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle.Moreover,different numerical simulations of the control induced model are carried out to observe the effects of the control strategies.It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.展开更多
In this paper, the model of tuberculosis （TB） with exogenous reinfection by Feng et al. （2000） is analyzed from the symmetry and singularities perspective.
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 obta...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.展开更多
文摘COVID-19 and Tuberculosis(TB)are among the major global public health problems and diseases with major socioeconomic impacts.The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated.In this study,we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB.Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria.Under certain conditions,the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one.The equilibria of the full TBCOVID-19 model are locally asymptotically stable,but not globally,due to the possible occurrence of backward bifurcation.The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R_(0)<1 and the 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 community.The optimal control strategies were proposed to minimize the disease burden and related costs.The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle.Moreover,different numerical simulations of the control induced model are carried out to observe the effects of the control strategies.It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.
文摘In this paper, the model of tuberculosis （TB） with exogenous reinfection by Feng et al. （2000） is analyzed from the symmetry and singularities perspective.
文摘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.
