Modelling the Impact of Migration on HIV Persistency in Ghana

  • Ofosuhene Okofrobour Apenteng Research Group for Genomic Epidemiology, National Food Institute, Technical University of Denmark, Denmark
  • Noor Azina Ismail Department of Applied Statistics, Faculty of Economics & Administration, University of Malaya, Kuala Lumpur, Malaysia
Keywords: HIV/AIDS, SI_1 I_2 A Model, Migration, Mathematical Transmission Modelling, Simulation


Migrants may be exposed to health risks before, during and after leaving their countries of origin. Unfortunately, knowledge about the health status of migrants is often limited because they are often excluded from surveys. This paper extends the susceptible-exposed-infective-removed model to handle the assumption of homogeneous mixing, the incorporation of migration and the induced death rates of the disease in modelling the spread of HIV/AIDS. These extensions demonstrate that the impact of migration on HIV persistency is critical when attempting to predict where and how fast the disease will propagate. The spectral analysis of a time series was used to determine the frequency at which the disease is spread and its equilibrium levels. The results indicate that with the persistent flow of migration into a country, the disease status changes from epidemic to endemic. If the direct flow of migration into the population is restricted, the persistent spread of the disease can be minimised.


UNAIDS report on the global AIDS epidemic, Global Report, 2013.

S. G. Deeks, S. R.Lewin, and D. V. Havlir, The end of AIDS: HIV infection as a chronic disease, The Lancet, 382(9903), pp.1525–1533, 2013.

K. S. Khan, D.Wojdyla, L. Say, A. M.Glmezoglu, and P. F. Van Look. WHO analysis of causes of maternal death: a systematic review, The lancet, 367(9516), pp.1066–1074, 2006.

C. D. Mathers and , D. Loncar, Projections of global mortality and burden of disease from 2002 to 2030. PLoS medicine, 3(11),e442, 2006.

Brummer, D. Labour Migration and HIV/AIDS in Southern Africa, International Organisation for Migration Regional Office for Southern Africa. pp. 1–26. 2002

M. Coffee, M.N. Lurie, and G.P. Garnett, Modelling the impact of migration on the HIV epidemic in South Africa, AIDS, 21(3): pp.343–350, 2007.

K. N. Deering, P. Vickerman, S. Moses, B. M. Ramesh, J. F. Blanchard and M. C. Boily, The impact of out-migrants and out -migration on the HIV/AIDS epidemic: a case study from south-west India. AIDS, 22: pp. 165–181, 2008.

E. A. Parrado, C. A. Flippen, and C. McQuiston, Use of commercial sex workers among Hispanic migrants in North Carolina:implications for the spread of HIV, Perspectives on sexual and reproductive health, 36(4), pp.150–156, 2004.

R. Naresh, A. Tripathi, and S. Omar, Modelling the spread of AIDS epidemic with vertical transmission, Applied Mathematics and Computation, 178(2): pp. 262–272, 2006.

O. O. Apenteng and Ismail, N. A. Ismail, A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection, PloS one,10(7), e0131950, 2015.

L. Corno and D. De Walque, Mines, migration and HIV/AIDS in Southern Africa, The World Bank, 2012.

M. T Mbizvo and M. T Bassett, Reproductive health and AIDS prevention in sub-Saharan Africa: the case for increased male participation, Health Policy and Planning, 11(1), pp.84–92, 1996.

P. Quartey, Migration in Ghana: A Country profile 2009, 2010.

UNHCR, Global Trends of asylum of refugees 2012: Table 18. Major mass inflows, 2012.

J. H. Jones, Notes On R0, Department of Anthropological Sciences: Califonia. pp. 17, 2007.

O. O. Apenteng and , N. A.Ismail, Modelling the spread of HIV and AIDS epidemic trends in male and female populations, World Journal of Modelling and Simulation, 13(3), pp.183–192, 2017.

S. Rosa and D. F Torres, Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic, Model with Application to HRSV in Florida. pp.140–149, 2018.

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180(1-2): pp. 29-48, 2005.

R. Naresh, A. Tripathi, and D. Sharma, A nonlinear HIV/AIDS model with contact tracing, Applied Mathematics and Computation, 217(23): pp. 9575–9591, 2011.

J. M. Gran, L.Wasmuth, E. J.Amundsen, B. H. Lindqvist, and O. O.Aalen, Growth rates in epidemic models: Application to a model for HIV/AIDS progression, Statistics in Medicine, 27(23): pp. 4817-4834, 2008.

T. Zhang, M. Jia, H. Luo, Y. Zhou, and N. Wang, Study on a HIV/AIDS model with application to Yunnan province, China Applied Mathematical Modelling, 35(9): pp. 4379–4392, 2011.

UNAIDS/WHO: Adult (15-49) HIV prevalence percent by country, 1990-2007, 2008 Report on the global AIDS epidemic, 2008.

A. Adlakha, International Brief. Population trends: Ghana, Department of Commerce United State, 2006.

F. Nyabadza, Z. Mukandavire, and S.D. Hove-Musekwa,Modelling the HIV/AIDS epidemic trends in South Africa: Insights from a simple mathematical model, Nonlinear Analysis: Real World Applications, 12(4): pp. 2091–2104, 2011.

Ghana - Death rate, crude, (per 1;000 People) in Ghana,, 2014.

UNICEF. State of the Worlds Children, Statistical Tables,, 2011

A. Galindro, and D. F.Torres, A simple mathematical model for unemployment: a case study in Portugal with optimal control. arXiv preprint arXiv:1801.00058, 2017.

R. Naresh, A. Tripathi, and D. Sharma, Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives, Mathematical and Computer Modelling, 49: pp. 880–892, 2009.

Comprehensive, Up-to-date Information on HIV/AIDS Treatment, Prevention, and Policy University of California San Francisco,, 2013

Team, R. C. R: A language and environment for statistical computing, 2013

How to Cite
Apenteng, O. O., & Ismail, N. A. (2019). Modelling the Impact of Migration on HIV Persistency in Ghana. Statistics, Optimization & Information Computing, 7(1), 55-65.
Research Articles