A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission
In this study, the co-infection of HIV and cholera model has been developed and analyzed. The new fractional-order derivative is applied and the behavior of the solution is interpreted. The order of new generalized fractional-order derivative implication is presented. A new method is incorporated to...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/7965145 |
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| author | Kumama Regassa Cheneke Koya Purnachandra Rao Gereme Kenassa Edesssa |
| author_facet | Kumama Regassa Cheneke Koya Purnachandra Rao Gereme Kenassa Edesssa |
| author_sort | Kumama Regassa Cheneke |
| collection | DOAJ |
| description | In this study, the co-infection of HIV and cholera model has been developed and analyzed. The new fractional-order derivative is applied and the behavior of the solution is interpreted. The order of new generalized fractional-order derivative implication is presented. A new method is incorporated to determine the forward bifurcation at a threshold R0=1. The developed method is used to determine the stability of steady-state points. The full model and the submodels’ disease-free equilibrium are locally asymptotically stable if the corresponding reproduction number is less than one and unstable if the production number is greater than one. The only HIV model exhibits forward bifurcation at the threshold point, R0=1. The numerical simulations solutions obtained using a new generalized fractional-order derivative shows that the total human population size approaches the disease-free equilibrium if the order of the fractional derivative is higher. Also, the simulated results show that the memory effects toward the invading disease are less whenever the order of the fractional derivative is near 0 but higher whenever the order of the fractional derivative is near 1. Furthermore, V. cholerae concentration in the environment increases whenever the intrinsic growth rate increases. The numerical solutions are carried out using MATLAB software. |
| format | Article |
| id | doaj-art-25c3f979f5d84168883be110a70bd4d1 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-25c3f979f5d84168883be110a70bd4d12025-02-03T01:20:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/7965145A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic TransmissionKumama Regassa Cheneke0Koya Purnachandra Rao1Gereme Kenassa Edesssa2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this study, the co-infection of HIV and cholera model has been developed and analyzed. The new fractional-order derivative is applied and the behavior of the solution is interpreted. The order of new generalized fractional-order derivative implication is presented. A new method is incorporated to determine the forward bifurcation at a threshold R0=1. The developed method is used to determine the stability of steady-state points. The full model and the submodels’ disease-free equilibrium are locally asymptotically stable if the corresponding reproduction number is less than one and unstable if the production number is greater than one. The only HIV model exhibits forward bifurcation at the threshold point, R0=1. The numerical simulations solutions obtained using a new generalized fractional-order derivative shows that the total human population size approaches the disease-free equilibrium if the order of the fractional derivative is higher. Also, the simulated results show that the memory effects toward the invading disease are less whenever the order of the fractional derivative is near 0 but higher whenever the order of the fractional derivative is near 1. Furthermore, V. cholerae concentration in the environment increases whenever the intrinsic growth rate increases. The numerical solutions are carried out using MATLAB software.http://dx.doi.org/10.1155/2022/7965145 |
| spellingShingle | Kumama Regassa Cheneke Koya Purnachandra Rao Gereme Kenassa Edesssa A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission International Journal of Mathematics and Mathematical Sciences |
| title | A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission |
| title_full | A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission |
| title_fullStr | A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission |
| title_full_unstemmed | A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission |
| title_short | A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission |
| title_sort | new generalized fractional order derivative and bifurcation analysis of cholera and human immunodeficiency co infection dynamic transmission |
| url | http://dx.doi.org/10.1155/2022/7965145 |
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