Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 May 13:8:e959.
doi: 10.7717/peerj-cs.959. eCollection 2022.

Mathematical COVID-19 model with vaccination: a case study in Saudi Arabia

Abeer D Algarni  1 , Aws Ben Hamed  2 , Monia Hamdi  1 , Hela Elmannai  1 , Souham Meshoul  1
Affiliations

Mathematical COVID-19 model with vaccination: a case study in Saudi Arabia

Abeer D Algarni et al. PeerJ Comput Sci. .

Abstract

The discovery of a new form of corona-viruses in December 2019, SARS-CoV-2, commonly named COVID-19, has reshaped the world. With health and economic issues at stake, scientists have been focusing on understanding the dynamics of the disease, in order to provide the governments with the best policies and strategies allowing them to reduce the span of the virus. The world has been waiting for the vaccine for more than one year. The World Health Organization (WHO) is advertising the vaccine as a safe and effective measure to fight off the virus. Saudi Arabia was the fourth country in the world to start to vaccinate its population. Even with the new simplified COVID-19 rules, the third dose is still mandatory. COVID-19 vaccines have raised many questions regarding in its efficiency and its role to reduce the number of infections. In this work, we try to answer these question and propose a new mathematical model with five compartments, including susceptible, vaccinated, infectious, asymptotic and recovered individuals. We provide theoretical results regarding the effective reproduction number, the stability of endemic equilibrium and disease free equilibrium. We provide numerical analysis of the model based on the Saudi case. Our developed model shows that the vaccine reduces the transmission rate and provides an explanation to the rise in the number of new infections immediately after the start of the vaccination campaign in Saudi Arabia.

Keywords: COVID-19; Mathematical model; Stability; Vaccination.

PubMed Disclaimer

Conflict of interest statement

The authors declare there are no competing interests.

Figures

Figure 1
Figure 1. The proposed model.
Figure 2
Figure 2. Varying R1 and R2 as a function of vaccination rate for two virus transmission rates, β = 0.233 and β = 0.462.
(A) Varying R1 and R2 as a function of ψ, β = 0.233 (B) Varying R1 and R2 as a function of ψ, β = 0.462
Figure 3
Figure 3. Number of active cases and recovered after infection in KSA, starting from 18/12/2020.
Figure 4
Figure 4. Percentage of susceptible (A), vaccinated (B), infectious (C), asymptomatic (D), and recovered (E) individuals. β = 0.233, ψ = 0.0012.
Figure 5
Figure 5. Percentage of susceptible (A), vaccinated (B), infectious (C), asymptomatic (D), and recovered (E) individuals. β = 0.462, ψ = 0.0012.
See this image and copyright information in PMC

References

    1. Aldila D, Khoshnaw SH, Safitri E, Anwar YR, Bakry AR, Samiadji BM, Anugerah DA, GH MFA, Ayulani ID, Salim SN. A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: the case of Jakarta, Indonesia. Chaos, Solitons & Fractals. 2020;139:110042. doi: 10.1016/j.chaos.2020.110042. - DOI - PMC - PubMed
    1. Alexander ME, Moghadas SM. Bifurcation analysis of an SIRS epidemic model with generalized incidence. SIAM Journal on Applied Mathematics. 2005;65(5):1794–1816. doi: 10.1137/040604947. - DOI
    1. Algehyne EA, Ibrahim M. Fractal-fractional order mathematical vaccine model of COVID-19 under non-singular kernel. Chaos, Solitons & Fractals. 2021;150:111150. doi: 10.1016/j.chaos.2021.111150. - DOI - PMC - PubMed
    1. Asamoah JKK, Jin Z, Sun G-Q, Seidu B, Yankson E, Abidemi A, Oduro F, Moore SE, Okyere E. Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions. Chaos, Solitons & Fractals. 2021;146:110885. doi: 10.1016/j.chaos.2021.110885. - DOI - PMC - PubMed
    1. Asamoah JKK, Nyabadza F, Jin Z, Bonyah E, Khan MA, Li MY, Hayat T. Backward bifurcation and sensitivity analysis for bacterial meningitis transmission dynamics with a nonlinear recovery rate. Chaos, Solitons & Fractals. 2020;140:110237. doi: 10.1016/j.chaos.2020.110237. - DOI

LinkOut - more resources