Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors
Abstract The monkeypox virus (MPXV), which is a member of the Orthopoxvirus genus in the class Poxviridae, is the causative agent of the zoonotic viral infection MPXV. The disease is similar to smallpox, but it is usually less dangerous. This study examines the evolution of the MPXV epidemic in Cana...
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2025-01-01
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| author | Saima Rashid Abdul Bariq Ilyas Ali Sobia Sultana Ayesha Siddiqa Sayed K. Elagan |
| author_facet | Saima Rashid Abdul Bariq Ilyas Ali Sobia Sultana Ayesha Siddiqa Sayed K. Elagan |
| author_sort | Saima Rashid |
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| description | Abstract The monkeypox virus (MPXV), which is a member of the Orthopoxvirus genus in the class Poxviridae, is the causative agent of the zoonotic viral infection MPXV. The disease is similar to smallpox, but it is usually less dangerous. This study examines the evolution of the MPXV epidemic in Canada with an emphasis on the effects of control employing actual data. The main challenge is accurately estimating the virus’s rate of transmission and assessing the effectiveness of vaccination campaigns. By taking into account the modified Atangana–Baleanu–Caputo (mABC) fractional difference operator, we develop an analytical framework for an outbreak caused by MPXV and broaden it to accommodate the fractional scenario. The non-negativity and boundedness are guaranteed by the computation of the fractional-order MPXV system. At the disease-free equilibrium (DFE) $$\mathcal {P}_{0}$$ , we perform a local asymptotical stability analysis (LAS) and display the outcome for $$\mathbb {R}_{0}<1$$ . When $$\mathbb {R}_{0\textrm{r}}>1$$ and $$\mathbb {R}_{0\hbar }<1$$ , the single endemic equilibrium point (EEP) of infectious rodents is globally asymptotically stable (GAS). Lyapunov’s approach and LaSalle’s invariant criterion demonstrate that the GAS in terms of EEP for infectious persons occurs when $$\mathbb {R}_{0\textrm{r}}<1$$ and $$\mathbb {R}_{0\hbar }>1$$ . Through the application of nonlinear least squares, we determine the parameter values applying actual cases collected from Canada. To further bolster the operator’s effectiveness, a number of tests of this novel kind of operator were conducted. We remark that in various time scale domains $$\mathbb {N}_{\ell }$$ , the investigated discrete formulations will be $$\rho ^{2}$$ -nonincreasing or $$\rho ^{2}$$ -nondecreasing by examining $$\rho$$ -monotonicity formulations and the basic properties of the suggested operator. Algorithms are constructed in the discrete generalized Mittag–Leffler (GML) kernel for mathematical simulations, emphasizing the effects of the infection resulting from multiple factors. The dynamical technique used to build the MPXV framework was significantly impacted by fractional-order. In order to lessen the infections, severity, five time-dependent control factors are also implemented. The optimality criteria are produced by applying Pontryagin’s maximal argument to prove the validity of the most effective control. Various combos of control factors are offered to reduce the incidence of MPXV. The results of the current research provide governmental officials and healthcare professionals with practical steps to take in order to establish efficient and ideal preventive approaches to reduce the MPXV outbreaks. |
| format | Article |
| id | doaj-art-6f65db17f8504dc8ab38ab8a67f8931a |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
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| spelling | doaj-art-6f65db17f8504dc8ab38ab8a67f8931a2025-01-26T12:27:51ZengNature PortfolioScientific Reports2045-23222025-01-0115114410.1038/s41598-024-83691-yDynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factorsSaima Rashid0Abdul Bariq1Ilyas Ali2Sobia Sultana3Ayesha Siddiqa4Sayed K. Elagan5Department of Mathematics, Government College UniversityDepartment of Mathematics, Laghman UniversityDepartment of Basic Sciences and Humanities, University of Engineering and Technology Lahore, Faisalabad CampusDepartment of Mathematics, Imam Mohammad Ibn Saud Islamic UniversityDepartment of Mathematics, Government College UniversityDepartment of Mathematics and Statistics, College of Science, Taif UniversityAbstract The monkeypox virus (MPXV), which is a member of the Orthopoxvirus genus in the class Poxviridae, is the causative agent of the zoonotic viral infection MPXV. The disease is similar to smallpox, but it is usually less dangerous. This study examines the evolution of the MPXV epidemic in Canada with an emphasis on the effects of control employing actual data. The main challenge is accurately estimating the virus’s rate of transmission and assessing the effectiveness of vaccination campaigns. By taking into account the modified Atangana–Baleanu–Caputo (mABC) fractional difference operator, we develop an analytical framework for an outbreak caused by MPXV and broaden it to accommodate the fractional scenario. The non-negativity and boundedness are guaranteed by the computation of the fractional-order MPXV system. At the disease-free equilibrium (DFE) $$\mathcal {P}_{0}$$ , we perform a local asymptotical stability analysis (LAS) and display the outcome for $$\mathbb {R}_{0}<1$$ . When $$\mathbb {R}_{0\textrm{r}}>1$$ and $$\mathbb {R}_{0\hbar }<1$$ , the single endemic equilibrium point (EEP) of infectious rodents is globally asymptotically stable (GAS). Lyapunov’s approach and LaSalle’s invariant criterion demonstrate that the GAS in terms of EEP for infectious persons occurs when $$\mathbb {R}_{0\textrm{r}}<1$$ and $$\mathbb {R}_{0\hbar }>1$$ . Through the application of nonlinear least squares, we determine the parameter values applying actual cases collected from Canada. To further bolster the operator’s effectiveness, a number of tests of this novel kind of operator were conducted. We remark that in various time scale domains $$\mathbb {N}_{\ell }$$ , the investigated discrete formulations will be $$\rho ^{2}$$ -nonincreasing or $$\rho ^{2}$$ -nondecreasing by examining $$\rho$$ -monotonicity formulations and the basic properties of the suggested operator. Algorithms are constructed in the discrete generalized Mittag–Leffler (GML) kernel for mathematical simulations, emphasizing the effects of the infection resulting from multiple factors. The dynamical technique used to build the MPXV framework was significantly impacted by fractional-order. In order to lessen the infections, severity, five time-dependent control factors are also implemented. The optimality criteria are produced by applying Pontryagin’s maximal argument to prove the validity of the most effective control. Various combos of control factors are offered to reduce the incidence of MPXV. The results of the current research provide governmental officials and healthcare professionals with practical steps to take in order to establish efficient and ideal preventive approaches to reduce the MPXV outbreaks.https://doi.org/10.1038/s41598-024-83691-yModified Atangana–Baleanu–Caputo fractional operatorMonkeypox virusNumerical simulationsComputational modelingComputational simulationsPontryagin’s maximal principle |
| spellingShingle | Saima Rashid Abdul Bariq Ilyas Ali Sobia Sultana Ayesha Siddiqa Sayed K. Elagan Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors Scientific Reports Modified Atangana–Baleanu–Caputo fractional operator Monkeypox virus Numerical simulations Computational modeling Computational simulations Pontryagin’s maximal principle |
| title | Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| title_full | Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| title_fullStr | Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| title_full_unstemmed | Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| title_short | Dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| title_sort | dynamic analysis and optimal control of a hybrid fractional monkeypox disease model in terms of external factors |
| topic | Modified Atangana–Baleanu–Caputo fractional operator Monkeypox virus Numerical simulations Computational modeling Computational simulations Pontryagin’s maximal principle |
| url | https://doi.org/10.1038/s41598-024-83691-y |
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