An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay
This paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease...
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| Format: | Article |
| Language: | English |
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Nigerian Society of Physical Sciences
2019-10-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/5 |
| _version_ | 1818392111608758272 |
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| author | L. Adamu N. Hussaini |
| author_facet | L. Adamu N. Hussaini |
| author_sort | L. Adamu |
| collection | DOAJ |
| description | This paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number, R0, is less than unity. Using time delay as a bifurcation parameter in the delay-differential version of the model, it has been shown that the incubation period has a significant effect on the stability of the equilibria and we derived the condition for Hopf bifurcation to occur. |
| first_indexed | 2024-12-14T05:24:13Z |
| format | Article |
| id | doaj.art-507d291c08504835a3259d5c12e153ee |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-12-14T05:24:13Z |
| publishDate | 2019-10-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-507d291c08504835a3259d5c12e153ee2022-12-21T23:15:35ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042019-10-011110.46481/jnsps.2019.5An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay L. Adamu0N. Hussaini1Department of Mathematical Sciences, Bayero University, Kano, Nigeria.Department of Mathematical Sciences, Bayero University, Kano, NigeriaThis paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number, R0, is less than unity. Using time delay as a bifurcation parameter in the delay-differential version of the model, it has been shown that the incubation period has a significant effect on the stability of the equilibria and we derived the condition for Hopf bifurcation to occur.https://journal.nsps.org.ng/index.php/jnsps/article/view/5ZVLStabilityHopf bifurcationTime delay |
| spellingShingle | L. Adamu N. Hussaini An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay Journal of Nigerian Society of Physical Sciences ZVL Stability Hopf bifurcation Time delay |
| title | An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay |
| title_full | An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay |
| title_fullStr | An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay |
| title_full_unstemmed | An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay |
| title_short | An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay |
| title_sort | epidemic model of zoonotic visceral leishmaniasis with time delay |
| topic | ZVL Stability Hopf bifurcation Time delay |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/5 |
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