The dynamics of hybrid-immune and immunodeficient susceptible individuals and the three stages of COVID-19 vaccination

E. A. Nwaibeh; M. K. M. Ali; M. O. Adewole

doi:10.46481/jnsps.2024.2001

Authors

E. A. Nwaibeh
emmanmath@gmail.com
aSchool of Mathematical Sciences, Universiti Sains Malaysia, 11700 Glugor, Pulau Penang Malaysia
M. K. M. Ali School of Mathematical Sciences, Universiti Sains Malaysia, 11700 Glugor, Pulau Penang Malaysia
M. O. Adewole School of Basic Sciences, Nigeria Maritime University Okerenkoko, 332105 Warri, Delta, Nigeria

Keywords:

COVID-19, Vaccination, Heterogeneous immunity, Parameter estimation, Optimal control

Abstract

The World Health Organization has disclosed that the hybrid-immune and immunodeficient individuals are two distinct classes of individuals susceptible to the COVID-19 virus. To model this unique characteristics of two distinct categories of susceptible individuals and the dynamics of the three phases of a vaccination program implemented by the World Health Organization in Malaysia, which have not been accounted for in previous studies, a twelve compartmental SSVEIHQR-D epidemiological model was developed. This model aimed to accurately capture the spread of the COVID-19 virus by fitting real-life data to the model and obtaining updated estimates of the reproduction number. The study also focused on assessing current control measures and exploring strategies to eradicate the virus and mitigate future outbreaks. Mathematical analyses of the model included investigations into stability, equilibrium points, the basic reproduction number R0, optimal control strategies, and sensitivity analyses. Estimation and fitting of the model parameters were conducted using daily situation reports from the Ministry of Health of Malaysia. The obtained value of the basic reproduction number, based on fitted parameter values, indicated stability and reflected the current pandemic situation more realistically. Additionally, the herd immunity threshold was calculated and interpreted in the context of the study findings. Finally, practical insights and recommendations derived from the model’s results were provided to inform government agencies, public health organizations, and intervention bodies, aimed at controlling the spread of the COVID-19 virus.

Dimensions

REFERENCES

A. Elengoe, “Covid-19 outbreak in Malaysia”, Osong public health and research perspectives 11 (2020) 93. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7258884/.

N. C. for Disease Control and Prevention, “An update of covid-19 out-break in Nigeria, disease situation reports”, 2023. [Online]. https://ncdc.gov.ng/diseases/sitreps.

C. Yang & J. Wang, “A mathematical model for the novel coronavirus epidemic in Wuhan, China”, Mathematical biosciences and engineering: MBE 17 (2020) 2708. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7376496/.

Wikipedia contributors, “Public health emergency of international concern — Wikipedia, the free encyclopedia”, 2023, [Online; accessed 16-October-2023]. [Online]. https://en.wikipedia.org/w/index.php?title=Publichealthemergencyofinternationalconcern&oldid=1170730852.

I. O. Joshua, “Understanding covid 19 attributable fraction in Nigeria”, Curr Tre Biosta & Biometr 2 (2020) 276. https://ideas.repec.org/a/abr/oactbb/v2y2020i5p276-277.html.

S. Anand & Y. Mayya, “Size distribution of virus laden droplets from expiratory ejecta of infected subjects”, Scientific reports, 10 (2020) 21174.https://www.nature.com/articles/s41598-020-78110-x.

P. Anfinrud, V. Stadnytskyi, C. E. Bax & A. Bax, “Visualizing speech generated oral fluid droplets with laser light scattering”, New England Journal of Medicine 382 (2020) 2061. https://www.nejm.org/doi/full/10.1056/nejmc2007800.

M. Jayaweera, H. Perera, B. Gunawardana & J. Manatunge, “Transmission of covid-19 virus by droplets and aerosols: A critical review on the unresolved dichotomy”, Environmental research 188 (2020) 109819. https://doi.org/10.1016/j.envres.2020.109819.

K. S. Kwon, J. I. Park, Y. J. Park, D. M. Jung, K. W. Ryu & J. H. Lee, “Erratum: Correction of text in the article ”evidence of long-distance droplet transmission of sars-cov-2 by direct air flow in a restaurant in Korea””, Journal of Korean medical science 36 (2021) 23. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7801146/.

C. C. Lai, S. Y. Chen, M. Y. Yen, P. I. Lee, W. C. Ko & P. R. Hsueh, “The impact of covid-19 preventative measures on airborne/droplet-transmitted infectious diseases in taiwan”, Journal of Infection 82 (2021) 30. https://doi.org/10.1016/j.jinf.2020.11.029.

Coronavirus disease (covid-19) pandemic, by WHO (2019). [Online]. https://www.who.int/emergencies/diseases/novel-coronavirus-2019.

O. J. Ibidoja & K. Rapheal Fowobaje, “Attributable fraction and forecasting for covid-19 confirmed cases in Nigeria using facebook- prophet machine learning model”, Asian Journal of Probability and Statistics 16 (2022) 1. https://sdiopr.s3.ap-south-1.amazonaws.com/doc/Rev AJPAS79418 Ssa A.pdf.

E. Nwaibeh & C. Chikwendu, “A deterministic model of the spread of scam rumor and its numerical simulations”, Mathematics and Computers in Simulation 207 (2023) 111. https://doi.org/10.1016/j.matcom.2022.12.024.

R. Ross, “An application of the theory of probabilities to the study of a priori pathometry.—part i”, Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character 92 (1916) 204. https://doi.org/10.1098/rspa.1916.0007.

R. Ross & H. P. Hudson, “An application of the theory of probabilities to the study of a priori pathometry.—part iii”, Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character 93 (1917) 225–24. https://doi.org/10.1098/rspa.1917.0015.

W. O. Kermack & A. G. McKendrick, “A contribution to the mathematical theory of epidemics”, Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character 115 (1927) 700. https://doi.org/10.1098/rspa.1927.0118.

D. G. Kendall, Deterministic and stochastic epidemics in closed populations, Proceedings of the third Berkeley symposium on mathematical statistics and probability, University of California Press Berkeley, 1956, pp. 149–165. https://digitalassets.lib.berkeley.edu/math/ucb/text/math s3 v4 article-08.pdf.

E. Nwaibeh, S. Kamara, S. Oladejo & H. Adamu, “Epidemiological model of computer malware prevalence and control”, Journal of the Nigerian Association of Mathematical Physics 49 (2019) 133. https://www.ajol.info/index.php/jonamp/article/view/196476.

A. De´nes & A. B. Gumel, “Modeling the impact of quarantine during an outbreak of ebola virus disease”, Infectious Disease Modelling 4 (2019) 12. https://doi.org/10.1016/j.idm.2019.01.003.

S. E. Eikenberry & A. B. Gumel, “Mathematical modeling of cli mate change and malaria transmission dynamics: a historical review”, Journal of mathematical biology 77 (2018) 857. https://doi.org/10.1007/s00285-018-1229-7.

C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. MacIntyre, M. H. Bonds & A. B. Gumel, “Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel coronavirus”, Mathematical biosciences 325 (2020) 108364. https://doi.org/10.1016/j.mbs.2020.108364.

M. O. Adewole, A. A. Onifade, F. A. Abdullah, F. Kasali & A. I. Ismail, “Modeling the dynamics of covid-19 in Nigeria”, International journal of applied and computational mathematics, vol. 7, pp. 1–25, 2021. [Online]. https://doi.org/10.1007/s40819-021-01014-5.

B. Omede, U. Odionyenma, A. Ibrahim & B. Bolaji, “Third wave of covid-19: mathematical model with optimal control strategy for reducing the disease burden in Nigeria”, International Journal of Dynamics and Control 11 (2023) 411. https://doi.org/10.1007/s40435-022-00982-w.

X. Zhu, B. Gao, Y. Zhong, C. Gu & K.-S. Choi, “Extended kalman filter based on stochastic epidemiological model for covid-19 modelling”, Computers in Biology and Medicine 137 (2021) 104810. https://doi.org/10.1016/j.compbiomed.2021.104810.

J. Danane, K. Allali, Z. Hammouch & K. S. Nisar, “Mathematical analysis and simulation of a stochastic covid-19 le´vy jump model with isolation strategy”, Results in Physics 23 (2021) 103994. https://doi.org/10.1016/j.rinp.2021.103994.

I. Ahmed, G. U. Modu, A. Yusuf, P. Kumam & I. Yusuf, “A mathematical model of coronavirus disease (covid-19) containing asymptomatic and symptomatic classes”, Results in physics 21 (2021) 103776. https://www.sciencedirect.com/science/article/pii/S2211379720321860.

M. Manaqib, M. Mahmudi & G. Prayoga, “Mathematical model and simulation of the spread of covid-19 with vaccination, implementation of health protocols, and treatment”, Jambura Journal of Biomathematics (JJBM) 4 (2023) 69. https://doi.org/10.34312/jjbm.v4i1.19162.

New studies find evidence of superhuman immunity to covid-19 in some individuals, by ALASKA Public Media, 2021. [Online]. https://alaskapublic.org/2021/09/07/new.

N. S. Nizami & C. Mujeebuddin, “Strong immunity-a major weapon to fight against covid-19”, IOSR J Pharm Biol Sci 15 (2020) 22.

https://www.iosrjournals.org/iosr-jpbs/papers/Vol15-issue3/Series-3/D1503032229.pdf.

G. Widjaja, A. T. Jalil, H. S. Rahman, W. K. Abdelbasset, D. O. Bokov, W. Suksatan, M. Ghaebi, F. Marofi, J. G. Navashenaq, F. Jadidi-Niaragh & M. Ahmadi, “Humoral immune mechanisms involved in protective and pathological immunity during covid-19”, Human Immunology 82 (2021) 733. https://doi.org/10.1016/j.humimm.2021.06.011.

L. A. Bienvenu, J. Noonan, X. Wang & K. Peter, “Higher mortality of covid-19 in males: sex differences in immune response and cardiovascular comorbidities”, Cardiovascular research 116 (2020) 2197. https: //doi.org/10.1093/cvr/cvaa284.

E. Paul, A. Steptoe & D. Fancourt, “Attitudes towards vaccines and intention to vaccinate against covid-19: Implications for public health communications”, The Lancet Regional Health–Europe 1 2021. https://doi.org/10.1016/j.lanepe.2020.100012.

G. Olsder & J. Van der Woude, Mathematical Systems Theory, Universitaire Pers, 2005. https://repository.tudelft.nl/islandora/object/uuid%3A99400a80-1e79-41dc-8e59-ce1c0bc20e15.

P. Van den Driessche & J. Watmough, “Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission”, Mathematical biosciences 180 (2002) 29. https://doi.org/10.1016/S0025-5564(02)00108-6.

M. Martcheva, An introduction to mathematical epidemiology, Springer, 2015, pp. 9–31. https://doi.org/10.1007/978-1-4899-7612-3.

A. A. M. Daud, “A note on lienard-chipart criteria and its application to epidemic models”, Mathematics and Statistics 9 (2021) 41. https://www.hrpub.org/download/20210130/MS7-13421295.pdf.

B. S. Gill, V. J. Jayaraj, S. Singh, S. Mohd Ghazali, Y. L. Cheong, N. H. Md Iderus, B. M. Sundram, T. B. Aris, H. Mohd Ibrahim, B. H. Hong & J. Labadin, “Modelling the effectiveness of epidemic control measures in preventing the transmission of covid-19 in Malaysia”, International Journal of Environmental Research and Public Health 17 (2020) 5509. https://doi.org/10.3390/ijerph17155509.

A. Abidemi, Z. M. Zainuddin & N. A. B. Aziz, “Impact of control interventions on covid-19 population dynamics in Malaysia: a mathematical study”, The European Physical Journal Plus 136 (2021) 1. https://doi.org/10.1140/epjp/s13360-021-01205-5.

K. Ganasegeran, A. S. H. Ch’ng & I. Looi, “What is the estimated covid 19 reproduction number and the proportion of the population that needs to be immunized to achieve herd immunity in Malaysia? a mathematical epidemiology synthesis”, Covid 1 (2021) 13. https://doi.org/10.3390/covid1010003.

R. R. Ibrahim & H. O. Oladipo, “Forecasting the spread of covid-19 in Nigeria using box-jenkins modeling procedure”, medRxiv (2020) 2020. https://doi.org/10.1101/2020.05.05.20091686.

D. Okuonghae & A. Omame, “Analysis of a mathematical model for covid-19 population dynamics in Lagos, Nigeria”, Chaos, Solitons & Fractals 139 (2020) 110032. https://doi.org/10.1016/j.chaos.2020.110032.

S. S. Negi, P. S. Rana, N. Sharma & M. S. Khatri, “A novel seiahr compartment model for accessing the impact of vaccination, intervention policies, and quarantine on the covid-19 pandemic: a case study of most affected countries Brazil, India, Italy, and USA”, Computational and Applied Mathematics 41 (2022) 305. https://doi.org/10.1007/s40314-022-01993-1.

Ministry of Health (MOH), “Open data on covid-19 in Malaysia”, 2023. [Online]. https://github.com/MoH-Malaysia/covid19-public.

S. Marino, I. B. Hogue, C. J. Ray & D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology”, Journal of theoretical biology 254 (2008) 178. https://doi.org/10.1016/j.jtbi.2008.04.011.

S. A. J. Marsden, L. S. S. Wiggins, L. Glass, R. Kohn & S. Sastry, Mathematical Physiology I: Cellular Physiology, Springer New York (NY), 2002, pp. 2196–9973.

https://link.springer.com/book/10.1007/978-0-387-75847-3.

J. Wang & C. Modnak, “Modeling cholera dynamics with controls”, Canadian applied mathematics quarterly 19 (2011) 255.

https://www.sci.nu.ac.th/new hris/researchDoc/doc/1/14-09-2013-15-36-54.pdf.

Using mathematics to understand and control the coronavirus pandemic, by Premium Times, 2020. [Online]. https://opinion.premiumtimesng.com/2020/05/04/u.

L. S. Pontryagin, Mathematical theory of optimal processes, CRC press,

London, 1987. https://doi.org/10.1201/9780203749319.