×

Global stability dynamics and sensitivity assessment of COVID-19 with timely-delayed diagnosis in Ghana. (English) Zbl 1494.92137

Summary: In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, \(\mathcal{R}_0\), for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on \(\mathcal{R}_0\). We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] W. H. Organization, WHO characterizes covid-19 as a pandemic„ https://www.who.int/dg/speeches/detail/who-director-general (2020).
[2] M. Moriyama, W. J. Hugentobler, A. Iwasaki, Seasonality of respiratory viral infections, Annual review of virology 7 (2020) 83-101.
[3] W. H. Organization, WHO weekly operational update on covid-19„ https://www.who.int/docs/default-source/coronaviruse/situation-reports (2020).
[4] J. Duncan, Two cases of coronavirus confirmed in ghana, citi newsroom (Retrieved 16 March 2020).
[5] J. K. K. Asamoah, C. Bornaa, B. Seidu, Z. Jin, Mathematical analysis of the effects of controls on transmission dynamics of sars-cov-2, Alexandria Engineering Journal 59 (6) (2020) 5069-5078.
[6] S. Djaoue, G. G. Kolaye, H. Abboubakar, A. A. A. Ari, I. Damakoa, Mathematical modeling, analysis and numerical simulation of the covid-19 transmission with mitigation of control strategies used in cameroon, Chaos, Solitons & Fractals 139 (2020) 110281. · Zbl 07505129
[7] M. A. Khan, A. Atangana, E. Alzahrani, et al., The dynamics of covid-19 with quarantined and isolation, Advances in Difference Equations 2020 (1) (2020) 1-22. · Zbl 1486.92242
[8] E. Alzahrani, M. El-Dessoky, D. Baleanu, Modeling the dynamics of the novel coronavirus using caputo-fabrizio derivative, Alexandria Engineering Journal 60 (5) (2021) 4651-4662.
[9] Z. Zhang, A. Zeb, S. Hussain, E. Alzahrani, Dynamics of covid-19 mathematical model with stochastic perturbation, Advances in Difference Equations 2020 (1) (2020) 1-12. · Zbl 1486.92308
[10] X. Rong, L. Yang, H. Chu, M. Fan, Effect of delay in diagnosis on transmission of covid-19, Math Biosci Eng 17 (3) (2020) 2725-2740. · Zbl 1470.92190
[11] Y. Fang, Y. Nie, M. Penny, Transmission dynamics of the covid-19 outbreak and effectiveness of government interventions: A data-driven analysis, Journal of medical virology 92 (6) (2020) 645-659.
[12] F. Ndaïrou, I. Area, J. J. Nieto, D. F. Torres, Mathematical modeling of covid-19 transmission dynamics with a case study of wuhan, Chaos, Solitons & Fractals 135 (2020) 109846. · Zbl 1489.92171
[13] J. K. K. Asamoah, M. A. Owusu, Z. Jin, F. Oduro, A. Abidemi, E. O. Gyasi, Global stability and cost-effectiveness analysis of covid-19 considering the impact of the environment: using data from ghana, Chaos, Solitons & Fractals 140 (2020) 110103. · Zbl 07508183
[14] E. Acheampong, E. Okyere, S. Iddi, J. H. Bonney, J. K. K. Asamoah, J. A. Wattis, R. L. Gomes, Mathematical modelling of earlier stages of covid-19 transmission dynamics in ghana, Results in Physics 34 (2022) 105193. doi:doi:10.1016/j.rinp.2022.105193. URL https://www.sciencedirect.com/science/article/pii/S2211379722000134
[15] S. Olaniyi, O. S. Obabiyi, K. Okosun, A. Oladipo, S. Adewale, Mathematical modelling and optimal cost-effective control of covid-19 transmission dynamics, The European Physical Journal Plus 135 (11) (2020) 938.
[16] L. Nkague Nkamba, T. T. Manga, Modelling and prediction of the spread of covid-19 in cameroon and assessing the governmental measures march − september2020, COVID 1 (3) (2021) 622-644. doi:10.3390/covid1030052. URL https://www.mdpi.com/2673-8112/1/3/52
[17] W. A. Halatoko, Y. R. Konu, F. A. Gbeasor-Komlanvi, A. J. Sadio, M. K. Tchankoni, K. S. Komlanvi, M. Salou, A. M. Dorkenoo, I. Maman, A. Agbobli, M. I. Wateba, K. S. Adjoh, E. Goeh-Akue, Y.-b. Kao, I. Kpeto, R. Pana, Paul Kinde-Sossou, A. Tamekloe, J. Nayo-Apétsianyi, S.-P. H. Assane, M. Prine-David, S. M. Awoussi, M. Djibril, M. Mijiyawa, A. C. Dagnra, D. K. Ekouevi, Prevalence of sars-cov-2 among high-risk populations in lomé togo in 2020, PLOS ONE 15 (11) (2020) 1-12. doi:10.1371/journal.pone.0242124. URL doi:10.1371/journal.pone.0242124
[18] C. H. Nkwayep, S. Bowong, B. Tsanou, M. A. A. Alaoui, J. Kurths, Mathematical modeling of covid-19 pandemic in the context of sub-saharan africa: a short-term forecasting in cameroon and gabon, Mathematical Medicine and Biology: A Journal of the IMA 39 (1) (2022) 1-48. arXiv:https://academic.oup.com/imammb/article-pdf/39/1/1/42576019/dqab020.pdf, doi:10.1093/imammb/dqab020. URL doi:10.1093/imammb/dqab020 · Zbl 1501.92181
[19] S. E. Moore, E. Okyere, Controlling the transmission dynamics of covid-19, Commun. Math. Biol. Neurosci. 2020 (6).
[20] Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, R. Ren, K. S. Leung, E. H. Lau, J. Y. Wong, et al., Early transmission dynamics in wuhan, china, of novel coronavirus-infected pneumonia, New England journal of medicine.
[21] S. Cheng, Y. Chen, W.and Yang, P. Chu, X. Liu, M. Zhao, W. Tan, L. Xu, Q. Wu, H. Guan, J. Liu, Effect of diagnostic and treatment delay on the risk of tuberculosis transmission in shenzhen, china: an observational cohort study, 1993-2010, PLoS One 8 (6) (2013) e67516.
[22] C. Kraef, A. Bentzon, A.and Panteleev, A. Skrahina, N. Bolokadze, S. Tetradov, R. Podlasin, I. Karpov, E. Borodulina, E. Denisova, I. Azina, Delayed diagnosis of tuberculosis in persons living with hiv in eastern europe: associated factors and effect on mortality—a multicentre prospective cohort study, BMC infectious diseases 21 (1) (2021) 1-12.
[23] A. Gumel, A. Enahoro, N. Calistus, A. Gideon, Mathematical assessment of the roles of vaccination and non-pharmaceutical interventions on covid-19 dynamics: a multigroup modeling approach, medRxiv (2021) 2020.12. 11.20247916.
[24] J. A. Jacquez, C. P. Simon, Qualitative theory of compartmental systems, Siam Review 35 (1) (1993) 43-79. · Zbl 0776.92001
[25] P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences 180 (1-2) (2002) 29-48. · Zbl 1015.92036
[26] Z. Shuai, P. van den Driessche, Global stability of infectious disease models using lyapunov functions, SIAM Journal on Applied Mathematics 73 (4) (2013) 1513-1532. · Zbl 1308.34072
[27] J. P. La Salle, The stability of dynamical systems, SIAM, 1976. · Zbl 0364.93002
[28] J. La Salle, S. Lefschetz, Stability by Liapunov’s direct method with applications by Joseph L Salle and Solomon Lefschetz, Elsevier, 2012. · Zbl 0098.06102
[29] H. I. Freedman, S. Ruan, M. Tang, Uniform persistence and flows near a closed positively invariant set, Journal of Dynamics and Differential Equations 6 (4) (1994) 583-600. · Zbl 0811.34033
[30] M. Y. Li, J. R. Graef, L. Wang, J. Karsai, Global dynamics of a seir model with varying total population size, Mathematical biosciences 160 (2) (1999) 191-213. · Zbl 0974.92029
[31] S. F. Abimbade, S. Olaniyi, O. Ajala, M. Ibrahim, Optimal control analysis of a tuberculosis model with exogenous re-infection and incomplete treatment, Optimal Control Applications and Methods 41 (6) (2020) 2349-2368. · Zbl 1469.92071
[32] O. S. Akanni, J. O., F. O. Akinpelu, Global asymptotic dynamics of a nonlinear illicit drug use system, J. Appl. Math. Comput. 66 (2021) 39-60. · Zbl 1475.92009
[33] S. Bowong, J. Tewa, Mathematical analysis of a tuberculosis model with differential infectivity, Communications in Nonlinear Science and Numerical Simulation 14 (11) (2009) 4010-4021. · Zbl 1221.34128
[34] A. Temgoua, Y. Malong, J. Mbang, S. Bowong, Global properties of a tuberculosis model with lost sight and multi-compartment of latents, Journal of Mathematical Modeling 6 (1) (2020) 47-76. · Zbl 1413.34179
[35] Worldometer, https://www.worldometers.info/coronavirus/country/ghana/, year = 02-09-2020.
[36] M. Martcheva, Introduction to Mathematical Epidemiology, Vol. 61, Springer, 2015. · Zbl 1333.92006
[37] W. P., Review total population, https://worldpopulationreview.com/ (2020).
[38] G. H. Service, COVID-19 Updates, Ghana., www.ghanahealthservice.org., [Retrieved 23 July 2020] (2020).
[39] H. H. Publishing., How long can the coronavirus that causes covid19 survive on surfaces, accessed 5th may 2020, https://www.health.harvard.edu/diseases-and-conditions/covid-19-basics, (2020).
[40] J. K. K. Asamoah, F. Nyabadza, Z. Jin, E. Bonyah, M. A. Khan, M. Y. Li, T. Hayat, Backward bifurcation and sensitivity analysis for bacterial meningitis transmission dynamics with a nonlinear recovery rate, Chaos, Solitons & Fractals 140 (2020) 110237. · Zbl 1495.92069
[41] J. Wu, R. Dhingra, M. Gambhir, J. V. Remais, Sensitivity analysis of infectious disease models: methods, advances and their application, Journal of The Royal Society Interface 10 (86) (2013) 20121018. doi:doi:10.1098/rsif.2012.1018.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.