Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis
Abstract
:1. Introduction
2. Methods
2.1. Mpox Outbreak Data
2.2. Mpoxv Model Description
2.3. Fundamental Properties of the Mpoxv Model
2.3.1. Positivity of Model Solutions
2.3.2. Invariant Region
3. Analytical Results
3.1. Disease-Free Equilibrium and Basic Reproduction Number
3.2. Basic Reproduction Number
3.3. Endemic Equilibrium and Its Stability
3.3.1. Endemic Equilibrium
3.3.2. Global Stability Analysis of the Endemic Equilibrium
3.4. Bifurcation Analysis
4. Numerical Results
4.1. Model Prediction
4.2. Numerical Simulations
4.3. Sensitivity Analysis
5. Concluding Remarks
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Variable | Description |
---|---|
Overall human population | |
Population of susceptible humans at high-risk | |
Population of susceptible humans at low-risk | |
Exposed humans | |
P | Populations of infectious humans in the prodromal stage |
Symptomatically mild infectious humans | |
Symptomatically severe infectious humans | |
H | Hospitalised humans |
Recovered humans | |
Total rodent population | |
Susceptible rodents | |
Exposed rodents | |
Infectious rodents | |
Recovered rodents | |
Parameter | |
Transmission rates/transmission probabilities | |
Modification parameters | |
Human recruitment rate (rodents) | |
Fraction of newly recruited humans moving to | |
v | Rate of reduction in infectiousness from |
Progression rates | |
Rate at which mpoxv progress from P to | |
Progression rate from mild to severe disease | |
Hospitalisation rates | |
mpoxv-induced death rates | |
Recovery rates | |
Human (rodents) natural death rate |
Parameter | Baseline (Range) | Units | Sources |
---|---|---|---|
– | Persons | [3,40] | |
Rodents | Assumed | ||
– | [3,40] | ||
– | [41] | ||
– | [3,24,42] | ||
– | [3,43,44] | ||
– | [45] | ||
v | – | Dimensionless | Estimated |
– | Estimated | ||
– | Estimated | ||
– | Estimated | ||
– | Dimensionless | [5] | |
– | Dimensionless | [5] | |
– | [44] | ||
– | [44] | ||
– | [5] | ||
– | Estimated | ||
– | Estimated | ||
– | Estimated | ||
– | [5] | ||
– | [5] | ||
– | [5] | ||
– | [44] | ||
– | [5] | ||
– | [5] | ||
– | [44] |
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Al-Shomrani, M.M.; Musa, S.S.; Yusuf, A. Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis. Mathematics 2023, 11, 1121. https://doi.org/10.3390/math11051121
Al-Shomrani MM, Musa SS, Yusuf A. Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis. Mathematics. 2023; 11(5):1121. https://doi.org/10.3390/math11051121
Chicago/Turabian StyleAl-Shomrani, Mohammed M., Salihu S. Musa, and Abdullahi Yusuf. 2023. "Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis" Mathematics 11, no. 5: 1121. https://doi.org/10.3390/math11051121
APA StyleAl-Shomrani, M. M., Musa, S. S., & Yusuf, A. (2023). Unfolding the Transmission Dynamics of Monkeypox Virus: An Epidemiological Modelling Analysis. Mathematics, 11(5), 1121. https://doi.org/10.3390/math11051121