{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T13:45:04Z","timestamp":1778507104187,"version":"3.51.4"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T00:00:00Z","timestamp":1542844800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007114","name":"African Institute for Mathematical Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007114","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MasterCard Foundation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2018,11,22]]},"abstract":"<jats:p>\n                    Human African trypanosomiasis (HAT), commonly known as sleeping sickness, is a neglected tropical vector-borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper, we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments, while in the human population, the HAT is modelled by four compartments. The next-generation matrix approach is used to derive the basic reproduction number,\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                      <mml:mrow>\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    , and it is also proved that if\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                      <mml:mrow>\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>\u2264<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    , the disease-free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persists in the population if the value of\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                      <mml:mrow>\n                        <mml:msub>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>&gt;<\/mml:mo>\n                        <mml:mn>1<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    . Furthermore, the optimal control model is determined by using the Pontryagin\u2019s maximum principle, with control measures such as education, treatment, and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures is very efficient and effective to eliminate HAT in Africa.\n                  <\/jats:p>","DOI":"10.1155\/2018\/5293568","type":"journal-article","created":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T19:51:24Z","timestamp":1542916284000},"page":"1-13","source":"Crossref","is-referenced-by-count":17,"title":["Mathematical Modelling of Human African Trypanosomiasis Using Control Measures"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1372-9610","authenticated-orcid":true,"given":"Hamenyimana Emanuel","family":"Gervas","sequence":"first","affiliation":[{"name":"African Institute for Mathematical Sciences, Biriwa, Cape Coast, Ghana"},{"name":"University of Dar es Salaam, Dar es Salaam, Tanzania"},{"name":"University of Dodoma, Dodoma, Tanzania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8086-8333","authenticated-orcid":true,"given":"Nicholas Kwasi-Do Ohene","family":"Opoku","sequence":"additional","affiliation":[{"name":"African Institute for Mathematical Sciences, Biriwa, Cape Coast, Ghana"},{"name":"University of Cape Coast, Cape Coast, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2535-7028","authenticated-orcid":true,"given":"Shamsuddeen","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"African Institute for Mathematical Sciences, Biriwa, Cape Coast, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1186\/s13071-015-1131-8"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2147\/clep.s39728"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/s0140-6736(09)60829-1"},{"key":"4","year":"2013"},{"key":"5","volume":"61","year":"2015"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1017\/s0031182000066853"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pntd.0001615"},{"key":"8","volume-title":"Modelling the control of tsetse and african trypanosomiasis through application of insecticides on cattle in Southeastern Uganda","year":"2013"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.12732\/ijpam.v88i1.10"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.172341"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1017\/s144618110000345x"},{"key":"12","volume-title":"A mathematical model to control the spread of malaria in Ghana","year":"2012"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0108172"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.12988\/ams.2014.45326"},{"key":"15","year":"1962"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19790590940"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1017\/s0031182010001496"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1142\/s0218339096000314"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2018\/5293568.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2018\/5293568.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2018\/5293568.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T19:51:26Z","timestamp":1542916286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/cmmm\/2018\/5293568\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,22]]},"references-count":18,"alternative-id":["5293568","5293568"],"URL":"https:\/\/doi.org\/10.1155\/2018\/5293568","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201810.0561.v1","asserted-by":"object"}]},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,22]]}}}