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Dynamic Analysis and Optimal Prevention Strategies for Monkeypox Spread Modeled via the Mittag--Leffler Kernel

Mine Yurtoğlu, Dilara Yapışkan, Ebenezer Bonyah, Beyza Billur İskender Eroğlu, Derya Avcı, Delfim F. M. Torres

TL;DR

The present study aims to discuss the indispensable effects of three control strategies such as vaccination, treatment, and quarantine to prevent the monkeypox epidemic modeled via the Atangana–Baleanu operator.

Abstract

Monkeypox is a viral disease belonging to the smallpox family. Although it has milder symptoms than smallpox in humans, it has become a global threat in recent years, especially in African countries. Initially, incidental immunity against monkeypox was provided by smallpox vaccines. However, the eradication of smallpox over time and thus the lack of vaccination has led to the widespread and clinical importance of monkeypox. Although mathematical epidemiology research on the disease is complementary to clinical studies, it has attracted attention in the last few years. The present study aims to discuss the indispensable effects of three control strategies such as vaccination, treatment, and quarantine to prevent the monkeypox epidemic modeled via the Atangana--Baleanu operator. The main purpose is to determine optimal control measures planned to reduce the rates of exposed and infected individuals at the minimum costs. For the controlled model, the existence-uniqueness of the solutions, stability, and sensitivity analysis, and numerical optimal solutions are exhibited. The optimal system is numerically solved using the Adams-type predictor--corrector method. In the numerical simulations, the efficacy of the vaccination, treatment, and quarantine controls is evaluated in separate analyzes as single-, double-, and triple-control strategies. The results demonstrate that the most effective strategy for achieving the aimed outcome is the simultaneous application of vaccination, treatment, and quarantine controls.

Dynamic Analysis and Optimal Prevention Strategies for Monkeypox Spread Modeled via the Mittag--Leffler Kernel

TL;DR

The present study aims to discuss the indispensable effects of three control strategies such as vaccination, treatment, and quarantine to prevent the monkeypox epidemic modeled via the Atangana–Baleanu operator.

Abstract

Monkeypox is a viral disease belonging to the smallpox family. Although it has milder symptoms than smallpox in humans, it has become a global threat in recent years, especially in African countries. Initially, incidental immunity against monkeypox was provided by smallpox vaccines. However, the eradication of smallpox over time and thus the lack of vaccination has led to the widespread and clinical importance of monkeypox. Although mathematical epidemiology research on the disease is complementary to clinical studies, it has attracted attention in the last few years. The present study aims to discuss the indispensable effects of three control strategies such as vaccination, treatment, and quarantine to prevent the monkeypox epidemic modeled via the Atangana--Baleanu operator. The main purpose is to determine optimal control measures planned to reduce the rates of exposed and infected individuals at the minimum costs. For the controlled model, the existence-uniqueness of the solutions, stability, and sensitivity analysis, and numerical optimal solutions are exhibited. The optimal system is numerically solved using the Adams-type predictor--corrector method. In the numerical simulations, the efficacy of the vaccination, treatment, and quarantine controls is evaluated in separate analyzes as single-, double-, and triple-control strategies. The results demonstrate that the most effective strategy for achieving the aimed outcome is the simultaneous application of vaccination, treatment, and quarantine controls.
Paper Structure (16 sections, 8 theorems, 89 equations, 3 figures, 1 algorithm)

This paper contains 16 sections, 8 theorems, 89 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Fundamental Definitions
  3. Model Formulation
  4. System Analysis
  5. The Feasibility of Region
  6. Existence and Uniqueness
  7. Stability Analysis
  8. Equilibrium Points
  9. Basic Reproduction Number
  10. Local Stability Analysis
  11. Optimal Control of Monkeypox
  12. Numerical Results and Discussion
  13. Strategy 1
  14. Strategy 2
  15. Strategy 3
  16. ...and 1 more sections

Key Result

Theorem 1

The region $\Omega =$$\Omega _{h}\times \Omega _{r}$ for the model eq11 such that and is a positive invariant set.

Figures (3)

  • Figure 1: A comparison for Strategy 1: Single control versus uncontrolled effects for $\alpha=0.90$.
  • Figure 2: A comparison for Strategy 2: double control versus uncontrolled effects for $\alpha=0.90$.
  • Figure 3: A comparison for Strategy 3: Triple control strategy versus the best double control strategy for $\alpha=0.90$.

Theorems & Definitions (22)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 12 more