Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization

Rubayyi T Alqahtani; Salihu S Musa; Abdullahi Yusuf

doi:10.1016/j.rinp.2022.105715

Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization

Results Phys. 2022 Aug:39:105715. doi: 10.1016/j.rinp.2022.105715. Epub 2022 Jun 14.

Authors

Rubayyi T Alqahtani¹, Salihu S Musa^{2

3}, Abdullahi Yusuf^{4

5}

Affiliations

¹ Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
² Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China.
³ Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey.
⁴ Department of Computer Engineering, Biruni University, Istanbul, Turkey.
⁵ Department of Mathematics, Federal University Dutse, Jigawa, Nigeria.

Abstract

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( $R_{0}$ ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when $R_{0} > 1$ under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the $R_{0}$ and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.

Keywords: COVID-19; Epidemiological modelling; Reproduction number; Vaccination; Vertical transmission.