Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate
In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for th...
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MDPI AG
2021-09-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/18/2186 |
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| author | Salah Alsahafi Stephen Woodcock |
| author_facet | Salah Alsahafi Stephen Woodcock |
| author_sort | Salah Alsahafi |
| collection | DOAJ |
| description | In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula>) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and the CHIKV endemic point is locally asymptotically stable if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained. |
| first_indexed | 2024-03-10T07:28:45Z |
| format | Article |
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| language | English |
| last_indexed | 2024-03-10T07:28:45Z |
| publishDate | 2021-09-01 |
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| series | Mathematics |
| spelling | doaj.art-28b21af36a0f4bc0b7ff2a31c8ef47c82023-11-22T14:04:35ZengMDPI AGMathematics2227-73902021-09-01918218610.3390/math9182186Mathematical Study for Chikungunya Virus with Nonlinear General Incidence RateSalah Alsahafi0Stephen Woodcock1School of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, AustraliaSchool of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, AustraliaIn this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula>) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and the CHIKV endemic point is locally asymptotically stable if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.https://www.mdpi.com/2227-7390/9/18/2186Chikungunya viruscellular infectiongeneral incidence rateLaSalle’s invariance principleLyapunov stabilityoptimal control |
| spellingShingle | Salah Alsahafi Stephen Woodcock Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate Mathematics Chikungunya virus cellular infection general incidence rate LaSalle’s invariance principle Lyapunov stability optimal control |
| title | Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate |
| title_full | Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate |
| title_fullStr | Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate |
| title_full_unstemmed | Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate |
| title_short | Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate |
| title_sort | mathematical study for chikungunya virus with nonlinear general incidence rate |
| topic | Chikungunya virus cellular infection general incidence rate LaSalle’s invariance principle Lyapunov stability optimal control |
| url | https://www.mdpi.com/2227-7390/9/18/2186 |
| work_keys_str_mv | AT salahalsahafi mathematicalstudyforchikungunyaviruswithnonlineargeneralincidencerate AT stephenwoodcock mathematicalstudyforchikungunyaviruswithnonlineargeneralincidencerate |