Modelling COVID-19 Transmission Dynamics in Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, R0. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when R0 < 1 via a candidate Lyapunov function. Using the SARS-CoV∗Corresponding authors Email addresses: Edward.Acheampong1@nottingham.ac.uk/eoacheampong@ug.edu.gh (Edward Acheampong), Jonathan.Wattis@nottingham.ac.uk (Jonathan A. D. Wattis), Rachel.Gomes@nottingham.ac.uk (Rachel L. Gomes) Preprint submitted to * 8th February 2021 ar X iv :2 10 2. 02 98 4v 1 [ qbi o. PE ] 5 F eb 2 02 1 2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube samplingrank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of R0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by R0 = 3.110, with the 95% confidence interval being 2.042 ≤ R0 ≤ 3.240, and the mean value being R0 = 2.623. Of the 32 parameters in the model, we find that just six have a significant influence onR0, these include the rate of testing, where an increasing testing rate contributes to the reduction of R0.

[1]  B. Buonomo.  Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model , 2020, Ricerche di Matematica.

[2]  G. Rohith,et al.  Dynamics and control of COVID-19 pandemic with nonlinear incidence rates , 2020, Nonlinear dynamics.

[3]  O Diekmann,et al.  The construction of next-generation matrices for compartmental epidemic models , 2010, Journal of The Royal Society Interface.

[4]  Rachel Waema Mbogo,et al.  Uncertainty and Sensitivity Analysis Applied to an In-Host Malaria Model with Multiple Vaccine Antigens , 2019, International Journal of Applied and Computational Mathematics.

[5]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[6]  S. Mushayabasa,et al.  On the role of governmental action and individual reaction on COVID-19 dynamics in South Africa: A mathematical modelling study , 2020, Informatics in Medicine Unlocked.

[7]  P. Colaneri,et al.  Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy , 2020, Nature Medicine.

[8]  Rita Ceppitelli,et al.  Epidemic evolution models to the test of Covid-19 , 2020, Bollettino della Unione matematica italiana.

[9]  Yixue Hao,et al.  The introduction of population migration to SEIAR for COVID-19 epidemic modeling with an efficient intervention strategy , 2020, Information Fusion.

[10]  TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA , 2020 .

[11]  Gul Zaman,et al.  Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class , 2020, BioMed research international.

[12]  J. Hyman,et al.  Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases , 2016 .

[13]  Rachel Waema Mbogo,et al.  SEIR model for COVID-19 dynamics incorporating the environment and social distancing , 2020, BMC Research Notes.

[14]  Rachel L. Gomes,et al.  Modelling emerging pollutants in wastewater treatment: A Case study using the pharmaceutical 17α-ethinylestradiol , 2019, Comput. Chem. Eng..

[15]  Hui Li,et al.  A Novel Coronavirus (COVID-19) Outbreak , 2020, Chest.

[16]  Maia Martcheva,et al.  An Introduction to Mathematical Epidemiology , 2015 .

[17]  Y. N. Kyrychko,et al.  Effects of latency and age structure on the dynamics and containment of COVID-19 , 2020, Journal of Theoretical Biology.

[18]  Syafruddin Side,et al.  Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia , 2020, Chaos, Solitons & Fractals.

[19]  M. G. Roberts,et al.  Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection , 2007, Journal of mathematical biology.

[20]  M. Imran,et al.  The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19 , 2020, Journal of biological dynamics.

[21]  Tridip Sardar,et al.  Assessment of lockdown effect in some states and overall India: A predictive mathematical study on COVID-19 outbreak , 2020, Chaos, Solitons & Fractals.

[22]  T. Hollingsworth,et al.  How will country-based mitigation measures influence the course of the COVID-19 epidemic? , 2020, The Lancet.

[23]  Radhika Dhingra,et al.  Sensitivity analysis of infectious disease models: methods, advances and their application , 2013, Journal of The Royal Society Interface.

[24]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

[25]  Mudassar Imran,et al.  Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone , 2015, Infectious Diseases of Poverty.

[26]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[27]  D G Altman,et al.  Statistics Notes: Measurement error proportional to the mean , 1996, BMJ.

[28]  J. Hyman,et al.  The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. , 2004, Journal of theoretical biology.

[29]  Zhen Jin,et al.  Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana , 2020, Chaos, Solitons & Fractals.

[30]  B. Rahman,et al.  The basic reproduction number of SARS‐CoV‐2 in Wuhan is about to die out, how about the rest of the World? , 2020, Reviews in medical virology.

[31]  Delfim F. M. Torres,et al.  Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan , 2020, Chaos, Solitons & Fractals.

[32]  M. R. Ferrández,et al.  Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China , 2020, Communications in Nonlinear Science and Numerical Simulation.

[33]  Yongli Cai,et al.  A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action , 2020, International Journal of Infectious Diseases.

[34]  K. Dietz.  The estimation of the basic reproduction number for infectious diseases , 1993, Statistical methods in medical research.

[35]  J. M. Carcione.  A simulation of a COVID-19 epidemic based on a deterministic SEIR model , 2020, medRxiv.

[36]  Junling Ma.  Estimating epidemic exponential growth rate and basic reproduction number , 2020, Infectious Disease Modelling.

[37]  Gerardo Chowell,et al.  Mathematical and statistical estimation approaches in epidemiology , 2009 .

[38]  Anas Abou-Ismail,et al.  Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists , 2020, SN Comprehensive Clinical Medicine.

[39]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[40]  Lianze Wang,et al.  Basic reproduction number and predicted trends of coronavirus disease 2019 epidemic in the mainland of China , 2020, Infectious Diseases of Poverty.

[41]  E. D. Sontag,et al.  A novel COVID-19 epidemiological model with explicit susceptible and asymptomatic isolation compartments reveals unexpected consequences of timing social distancing , 2020, Journal of Theoretical Biology.

[42]  Early stage COVID-19 disease dynamics in Germany: models and parameter identification , 2020, Journal of mathematics in industry.

[43]  M. Fan,et al.  Effect of delay in diagnosis on transmission of COVID-19. , 2020, Mathematical biosciences and engineering : MBE.

[44]  Jing Zhao,et al.  Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia , 2020, The New England journal of medicine.