A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease
A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-01-01
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| Series: | Journal of Biological Dynamics |
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| Online Access: | http://dx.doi.org/10.1080/17513758.2017.1418028 |
| _version_ | 1818279463069155328 |
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| author | Hsiu-Chuan Wei |
| author_facet | Hsiu-Chuan Wei |
| author_sort | Hsiu-Chuan Wei |
| collection | DOAJ |
| description | A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful, (c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment. |
| first_indexed | 2024-12-12T23:33:43Z |
| format | Article |
| id | doaj.art-9eaf5cb61d0145ffa53aefc509b7dcd3 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-12T23:33:43Z |
| publishDate | 2018-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-9eaf5cb61d0145ffa53aefc509b7dcd32022-12-22T00:07:36ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662018-01-0112119421010.1080/17513758.2017.14180281418028A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without diseaseHsiu-Chuan Wei0Feng Chia UniversityA previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful, (c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment.http://dx.doi.org/10.1080/17513758.2017.1418028competition modelbifurcation analysiscancerdynamical systemnumerical simulation |
| spellingShingle | Hsiu-Chuan Wei A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease Journal of Biological Dynamics competition model bifurcation analysis cancer dynamical system numerical simulation |
| title | A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease |
| title_full | A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease |
| title_fullStr | A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease |
| title_full_unstemmed | A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease |
| title_short | A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease |
| title_sort | mathematical model of tumour growth with beddington deangelis functional response a case of cancer without disease |
| topic | competition model bifurcation analysis cancer dynamical system numerical simulation |
| url | http://dx.doi.org/10.1080/17513758.2017.1418028 |
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