Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle
Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/2941961 |
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| author | Saul C. Mpeshe |
| author_facet | Saul C. Mpeshe |
| author_sort | Saul C. Mpeshe |
| collection | DOAJ |
| description | Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ0 is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order α=1,0.75,0.5, and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of α decreases. The infected population decreases with a decrease in the value of α. However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for α=1. Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics. |
| format | Article |
| id | doaj-art-fdb95f09c11e4584bfbbb37237ea54fd |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fdb95f09c11e4584bfbbb37237ea54fd2025-02-03T01:21:27ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/29419612941961Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic CycleSaul C. Mpeshe0Department of Mathematical Sciences, University of Iringa, P. O. Box 200, Iringa, TanzaniaRift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ0 is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order α=1,0.75,0.5, and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of α decreases. The infected population decreases with a decrease in the value of α. However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for α=1. Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics.http://dx.doi.org/10.1155/2021/2941961 |
| spellingShingle | Saul C. Mpeshe Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle Discrete Dynamics in Nature and Society |
| title | Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle |
| title_full | Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle |
| title_fullStr | Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle |
| title_full_unstemmed | Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle |
| title_short | Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle |
| title_sort | fractional order derivative model of rift valley fever in urban peridomestic cycle |
| url | http://dx.doi.org/10.1155/2021/2941961 |
| work_keys_str_mv | AT saulcmpeshe fractionalorderderivativemodelofriftvalleyfeverinurbanperidomesticcycle |