COVID-19 Model with High- and Low-Risk Susceptible Population Incorporating the Effect of Vaccines

Alhassan Ibrahim, Usa Wannasingha Humphries, Amir Khan, Saminu Iliyasu Bala, Isa Abdullahi Baba, Fathalla A. Rihan

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


It is a known fact that there are a particular set of people who are at higher risk of getting COVID-19 infection. Typically, these high-risk individuals are recommended to take more preventive measures. The use of non-pharmaceutical interventions (NPIs) and the vaccine are playing a major role in the dynamics of the transmission of COVID-19. We propose a COVID-19 model with high-risk and low-risk susceptible individuals and their respective intervention strategies. We find two equilibrium solutions and we investigate the basic reproduction number. We also carry out the stability analysis of the equilibria. Further, this model is extended by considering the vaccination of some non-vaccinated individuals in the high-risk population. Sensitivity analyses and numerical simulations are carried out. From the results, we are able to obtain disease-free and endemic equilibrium solutions by solving the system of equations in the model and show their global stabilities using the Lyapunov function technique. The results obtained from the sensitivity analysis shows that reducing the hospitals’ imperfect efficacy can have a positive impact on the control of COVID-19. Finally, simulations of the extended model demonstrate that vaccination could adequately control or eliminate COVID-19.

Original languageEnglish
Article number3
Issue number1
Publication statusPublished - Jan 2023


  • COVID-19
  • equilibrium solutions
  • global stability
  • sensitivity
  • stability analysis
  • vaccine

ASJC Scopus subject areas

  • Immunology
  • Pharmacology
  • Drug Discovery
  • Infectious Diseases
  • Pharmacology (medical)


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