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This assumed not only a stable reproduction number, but that known cases were just 40% of the total (based on the gap between the baseline model and figures for the number of people in treatment on a single day in August).By presenting such grim projections, the experts arguably made it less likely that they would come to pass.
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We present the evidence that the endemic equilibrium (EE) point is locally asymptotically stable when reproduction number (R_{0} > 1).
The disease-free equilibrium point results to be locally asymptotically stable if the reproduction number is less than unity while the endemic equilibrium point is locally asymptotically stable if such a number exceeds unity.
For the case when the efficacy of quarantine to prevent infection during quarantine is perfect, the disease-free equilibrium is globally-asymptotically stable when the reproduction threshold is less than unity.
For the malaria model with nonlinear incidence rate, it is shown that this phenomenon does not occur and the disease-free equilibrium of the model is globally-asymptotically stable whenever the reproduction number is less than unity.
For the case where infection with one strain confers complete immunity against infection with the other strain, it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the reproduction number is less than unity.
We proved that the deterministic model has a unique endemic equilibrium, which is asymptotically stable if the reproduction number R 0 is greater than one; this means that the disease will persist at the endemic equilibrium level if it is initially present and the disease die out if R 0 ⩽ 1.
Our results show that the disease-free equilibrium is globally stable when the basic reproduction number (R_{0}<1) and is unstable when (R_{0}>1).
In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity.
Moreover, we shall show that the disease free equilibrium of the model is globally asymptotically stable when the basic reproduction number (R_{0}) is less than 1, which is well consistent with the threshold property of the basic reproduction number.
We have shown that the disease free equilibrium is globally asymptotically stable when the basic reproduction number (R_{0}) is less than 1, which is well consistent with the threshold property of the basic reproduction number.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com