Reproduction numbers and subthreshold endemic equilibria for compartment models of disease transmission
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✨A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations.
✨It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable.
✨Thus, R0 is a threshold parameter for the model.
✨An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one.
✨This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models.
✨The results are significant for disease control.
Hope the information provided above is helpful ☺️
Here's the answer ⤵️
✨A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations.
✨It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable.
✨Thus, R0 is a threshold parameter for the model.
✨An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one.
✨This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models.
✨The results are significant for disease control.
Hope the information provided above is helpful ☺️
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