COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines
Abstract
:1. Introduction
2. Model Formulation
3. Model Analysis
3.1. Disease Free Equilibrium
3.2. Endemic Equilibrium
Global Stability Analysis of the Endemic Equilibrium
4. Numerical Simulations
Sensitivity Analysis
5. Extended Model with Vaccination
- i.
- The number of high-risk individuals reduces.
- ii.
- Infections can be prevented with some degree of efficacy.
The Effect of Vaccine on the Disease Dynamics
6. Discussion and Conclusions
- (i)
- A GAS DFE occurs in the model without vaccination every time the associated basic reproduction number is less than 1 and there are multiple endemic equilibria, which is a GAS in a particular case.
- (ii)
- Based on numerical simulations it is indicated that if some high-risk individuals were vaccinated and moved to low-risk, the disease could be reduced to a minimum. However, this is dependent on the coverage of vaccinations.
- (iii)
- The Latin Hypercube Sampling to create 1000 samples and the resulting Partial Rank Correlation Coefficients (PRCCs) were used to perform a sensitivity study of the model parameter values. A tornado plot is used to visually display the results. The parameters , (hospitalized recovery rate), , (reduction in infectiousness of risk individuals), according to sensitivity analysis, greatly lessen an epidemic if increased. However, if the rates of person-to-person interaction and hospital inefficacy are reduced, transmission also decreases.
Future Work Directions
- Some new models with a different approach of incidence fraction can be proposed.
- Several dynamical features of COVID-19 were captured by our model, though other population compartments might be added and furthermore implement optimal control strategies when having access to more detailed and authentic COVID-19 data.
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
COVID-19 | Coronavirus disease 2019 |
NPIs | Non-pharmaceutical interventions against COVID-19 |
DFE | Disease-free equilibrium |
EE | Endemic equilibrium |
LAS | Locally asymptotically stable |
GAS | Globally asymptotically stable |
SaSAT | Sampling and sensitivity analysis tool |
PRCC | Partial rank correlation coefficient |
LHS | Latin hypercube sampling |
ASQ | Alternative state quarantine |
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Variables | Description |
---|---|
Number of high-risk susceptible population | |
Number of low-risk susceptible population | |
E | Number of exposed population |
I | Number of infected population |
H | Number of hospitalize population |
R | Number of recovered population |
N | Total human population |
Parameter | Description |
---|---|
Recruitment rate | |
Effective contact rate | |
Fraction of newly recruited individuals moving to | |
Rate of reduction in infectiousness in | |
Rate of reduction in infectiousness in | |
The natural death rate | |
The rate of progression from exposed population to infected population | |
The rate of hospital inefficacy | |
The recovery rate of infected in | |
The hospitalization rate of infected individuals | |
The recovery rate of the hospitalized individuals | |
The COVID-19 induced mortality rate |
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Ibrahim, A.; Humphries, U.W.; Khan, A.; Iliyasu Bala, S.; Baba, I.A.; Rihan, F.A. COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines. Vaccines 2023, 11, 3. https://doi.org/10.3390/vaccines11010003
Ibrahim A, Humphries UW, Khan A, Iliyasu Bala S, Baba IA, Rihan FA. COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines. Vaccines. 2023; 11(1):3. https://doi.org/10.3390/vaccines11010003
Chicago/Turabian StyleIbrahim, Alhassan, Usa Wannasingha Humphries, Amir Khan, Saminu Iliyasu Bala, Isa Abdullahi Baba, and Fathalla A. Rihan. 2023. "COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines" Vaccines 11, no. 1: 3. https://doi.org/10.3390/vaccines11010003
APA StyleIbrahim, A., Humphries, U. W., Khan, A., Iliyasu Bala, S., Baba, I. A., & Rihan, F. A. (2023). COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines. Vaccines, 11(1), 3. https://doi.org/10.3390/vaccines11010003