Coupling and Synchronization of HIV/AIDS Fisher folk Metapopulations

Authors

  • Titus Rotich

    Moi UniversityP.O. BOX 3900 - 30100ELDORET - KENYA

  • Jacob Chepkwony

    University of Eldoret, P.O. Box 1125 - 30100, Eldoret

  • Robert Lagat

    South Eastern Kenya University, P.O. Box 23, Kitui

  • Jacob Bitok

    University of Eldoret, P.O. Box 1125 - 30100, Eldoret

Received date: August 31, 2022

Accepted date: October 4, 2022

Published date: November 24, 2022

DOI:

https://doi.org/10.14419/ijamr.v11i2.32166

Abstract

The study of epidemiology is often done with an assumption that the population is homogeneously mixed, and the disease dynamics is uniform. However, this is not always true, and cultural beliefs and economic activities significantly contribute to segregation not necessarily in spatial dimension but on the way of life. In this study, the dynamics of HIV/AIDS is studied in four distinct fisher-folk population patches, both individually and under all-to-all diffusive coupling. It was found that, the dynamics of each patch is periodic, and there exist an attracting invariant stable synchronization manifold. The manifold of the coupled system displayed robustness under small perturbation, even with a small coupling strength of k≪1. This guarantees uniformity of long term metapopulation disease dynamics.

Author Biography

  • Titus Rotich, Moi UniversityP.O. BOX 3900 - 30100ELDORET - KENYA

    Head of Subject

    Mathematics Department

References

  1. Jesse, M., et al., A fully coupled, mechanistic model for infectious disease dynamics in a metapopulation: movement and epidemic duration. Journal of theoretical biology, 2008. 254(2): p. 331-338.
  2. Allen, L.J., et al., Mathematical epidemiology. Vol. 1945. 2008: Springer.
  3. Olsen, L.F., G.L. Truty, and W.M. Schaffer, Oscillations and chaos in epidemics: a nonlinear dynamic study of six childhood diseases in Copenha-gen, Denmark. Theoretical population biology, 1988. 33(3): p. 344-370.
  4. Murray, J.D., Mathematical biology: I. An introduction. Vol. 17. 2007: Springer Science & Business Media.
  5. Keeling, M.J. and P. Rohani, Modeling infectious diseases in humans and animals. 2011: Princeton University Press.
  6. Strogatz, S., H and R. Mirollo, E, Synchronization of Pulse-Coupled Biological Oscillators. SIAM J APPL MATHS, 1990. 8(6): p. 1645 - 1662.
  7. Wasike, A.A. and K. Rotich, Synchronization and persistence in Diffusively Coupled Lattice Oscillators. 2007.
  8. Control, C.f.D. and Prevention, Epidemiology of HIV/AIDS--united states, 1981-2005. MMWR. Morbidity and mortality weekly report, 2006. 55(21): p. 589-592.
  9. Abu-Radded, L., Dual infection with HIV and malaria fuels the spread of both diseases in sub-Saharan Africa. Science, 2007. 315(5812): p. 598.
  10. WHO, W.H.O., 2008 Report on the Global AIDS Epidemic. 2008: World Health Organization.
  11. Kissling, E., et al., Fisherfolk are among groups most at risk of HIV: cross-country analysis of prevalence and numbers infected. Aids, 2005. 19(17): p. 1939-1946.
  12. Olowosegun, T., et al., Sexuality and HIV/AIDS among Fisher folks in Kainji Lake Basin. Global Journal of Medical Research Diseases, 2013. 13(2): p. 4-18.
  13. Tanzarn, N. and C. Bishop-Sambrook, The dynamics of HIV/AIDS in small-scale fishing communities in Uganda. Rome, Italy: HIV/AIDS Pro-gramme, Food and Agriculture Organization (FAO) of the United Nations, 2003.
  14. Kamali, A., et al., Heterogeneity of HIV incidence: a comparative analysis between fishing communities and in a neighbouring rural general popula-tion, Uganda, and implications for HIV control. Sexually transmitted infections, 2016. 92(6): p. 447-454.
  15. Woodhead, A.J., et al., Health in fishing communities: A global perspective. Fish and Fisheries, 2018. 19(5): p. 839-852.
  16. Béné, C. and S. Merten, Women and fish-for-sex: transactional sex, HIV/AIDS and gender in African fisheries. World development, 2008. 36(5): p. 875-899.
  17. Huang, M. HIV/AIDS among fishers: vulnerability of their partners. in Global symposium on women in fisheries. 2002. ICLARM‐WorldFish Cen-ter.
  18. Duwal, S., et al., Vulnerability of fishing communities to HIV/AIDS and impact on fish productivity in Nigeria. IOSR-JAVS, 2015. 8(2): p. 52-9.
  19. Allison, E.H. and J.A. Seeley, HIV and AIDS among fisherfolk: a threat to ‘responsible fisheries'? Fish and fisheries, 2004. 5(3): p. 215-234.
  20. Awuonda, M., The Voices of Dunga: Critical Study of Lake Victoria Fisherfolk and Their Perspectives on Fishery Management, Globalisation and Environmental Crises on Their Livelihoods and Local Institutions. 2003: Swedish University of Agricultural Science.
  21. Heagy, J., T. Carroll, and L. Pecora, Synchronous chaos in coupled oscillator systems. Physical Review E, 1994. 50(3): p. 1874.
  22. Sun, J., E.M. Bollt, and T. Nishikawa, Constructing generalized synchronization manifolds by manifold equation. SIAM Journal on Applied Dy-namical Systems, 2009. 8(1): p. 202-221.
  23. Josic, K., Synchronization of chaotic systems and invariant manifolds. Nonlinearity, 2000. 13(4): p. 1321.

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How to Cite

Rotich, T., Chepkwony, J., Lagat, R., & Bitok, J. (2022). Coupling and Synchronization of HIV/AIDS Fisher folk Metapopulations. International Journal of Applied Mathematical Research, 11(2), 35-42. https://doi.org/10.14419/ijamr.v11i2.32166

Received date: August 31, 2022

Accepted date: October 4, 2022

Published date: November 24, 2022