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To prevent the spread of the infectious disease, many researchers [33 36] began to investigate a treatment function in the epidemic models.
We give a treatment function satisfying (H1) as follows: h(I =left { textstylebegin{array}{l@{quad}l} c_{1} I,&Ileq I_{0}, c_{2} I,&I>I_{0}, end{array}displaystyle right.
Susceptible Exposed Infectious and Recovered epidemic model endowed with a treatment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease.
The nine Comprehensive Cancer Centres, covering the whole Netherlands, are regional network organisations of health-care professionals and institutes for cancer and palliative care aiming at improving cancer care through research, guideline development, knowledge exchange and organisational improvement without having a treatment function themselves.
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Avoiding the Hawthorne effect is supposed to provide a more realistic picture of how a treatment functions in everyday practice.
In the next section, we will construct the model and introduce the main assumptions for a discontinuous treatment function.
Unlike previous SEIR epidemic models, we are interested in finding the impact of the adoption of a discontinuous treatment function.
In 2008, Zhang et al. [40] introduced a saturated treatment function T(I =frac{beta I}{1+alpha I} (4) into the (SIR) model, where (beta>0), (alphageq0).
In 2011, Eckalbar et al. [39] adopted a quadratic treatment function T(I =maxbigl{ beta I-gI^{2}, 0bigr},quad beta, g>0 into the (SIR) epidemic model and found four equilibria at most.
In 2004, Wang et al. [37] introduced a constant treatment function begin{aligned} T(I)= textstylebegin{cases} beta,&I>0, 0,& I=0 end{cases}displaystyle end{aligned} into the (SIR) epidemic model.
Health related quality of life (HRQOL) is defined as a patient's perception of the impact of the disease and treatment functioning in a variety of dimensions including physical, mental and social domains [ 2].
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