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The effect of risk factor misclassification on the partial population attributable risk.
Then, if any partial population is negative, it is zero at some previous time instant.
The analysis in this paper is guided by a theoretical framework of technology adoption under partial population exposure proposed by Diagne and Demont (2007).
Intensity of the long-wavelength component of the exciton band attributed to the trans conformation increases with the temperature and with excitation wavelength indicating partial population of this state via thermally activated energy transfer.
Assume that the SVEIRS model is positive (in the sense that no partial population reaches a negative value for any time under nonnegative initial conditions) and, furthermore, that the susceptible and vaccinated populations remain positive for all time.
If any of the above right-hand-side integrals with upper-limit does not exist, then the corresponding limit of the involved partial population as time tends to infinity does not exist and, then, the limit value has to be replaced by the existing limit superior as time tends to infinity.
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Thus, there is a unique endemic equilibrium point with all the partial populations being nonnegative.
First note that all the partial populations are defined by continuous-time differentiable functions from (1.1)–(1.1).
Also, all of the partial populations, the whole population and the vaccination control function are non-negative for all time.
Note that if Theorems 4.2 and 4.3 hold then all the limit values at infinity of the partial populations exist since the total population is uniformly bounded and all the partial populations are nonnegative for all time.
As these are all partial populations, the positivity of the controlled SEIR-model combined with the observer is preserved.
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