Herpes Simplex Virus Type -2 (HSV-2) and HIV Co-infection Dynamics with Optimal Control
DOI:
https://doi.org/10.62054/ijdm/0101.09Abstract
Herpes Simplex Virus type-2 (HSV-2) is a member of the human Herpe is virial family, a set of viruses that produce viral infection in majority of humans. It is frequently unrecognized lifelong infection which may facilitate the Human Immunodeficiency Virus (HIV) transmission. In this paper, a deterministic co-infection model of HSV-2 and HIV was considered. The model was qualitatively analysed and numerically simulated. Optimal control theory was applied. We proved existence of the optimal control and characterized the controls. The controls represent monitoring and counselling of individuals infected with HSV-2 only and also represent monitoring and counselling of individuals dually infected with HSV-2 and HIV. It was revealed that efforts should be devoted to individuals dually infected with HSV-2 and HIV as compared to those infected with HSV-2 only.
Co-infection, Herpes, HIV, Optimal control, Reproduction number
References
Abu-Raddad, L. J., Magaret, A. S., and Celum, C. (2008). Genital herpes has played a more important role than any other sexually transmitted infections in driving HIV prevalence to Africa. Plos One, 3(5).
Bangsberg, D. R., Perry, S., Charlebois, E. D., Clark, R. A., Robertson, M., Zolopa, A. R., and Moss, A. (2001). Non-adherence to highly active antiretroviral therapy predicts progression to AIDS. AIDS, 15(9).
Bhunu, C. P., Garira, W., and Mukandavire, Z. (2009). Modelling HIV/AIDS and tuberculosis confection. Bulletin of Mathematical Biology, 71, 1745-1780.
Blower S., and Ma, L. (2004). Calculating the contribution of herpes simplex virus type 2 epidemics to increasing HIV incidence: Treatment implications. Clin. Infect, 39(5).
Blower, S. M., Porco, P. T., and Garby, G. (1998). Predicting and preventing the emergence of antiviral drug resistance in HSV-2. Nature Medicine, 4(6).
Carr, J. (1981). Applications of center manifold theory. New York: Springer-Verlag.
Castillo-Chavez, C., Feng, Z., and Huang, W. (2002). On the computation of R_0 and its role on global stability, in mathematical approaches for emerging and reemerging infectious diseases: Models, methods, and theory. Castillo-Chavez, C. Ed. IMA, 126(215-240).
Castillo-Chavez, C., and Song, B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2).
Feng, Z., Qui, Z., Sang, Z., Lorenzo, C., and Glasser, J. (2013). Modelling the Synergy between HSV-2 and HIV and potential impact of HSV-2 therapy. Mathematical Biosciences, 245(2).
Fleming, W., and Rishel, R. (1975). Deterministic and stochastic optimal control, Springer. Retrieved from Http://cds.cern.ch/Record/1611958.
Foss, A. M., Vickerman, P. T., Chalabi, Z., Mayaud, P., Alary, M., and Watts, C. H. (2009). Dynamic modelling of herpes simplex virus type-2 (HSV-2) transmission: Issue on structure uncertainty. Bulletin of Mathematical Biology, 71(3).
Freeman, E. E., Weiss, H. A., Glynn, J. R., Cross, P. L., Whitworth, J. A., and Hayes, R. J. (2006). Herpes simplex virus to infection increases HIV acquisition in men and women: Systematic review and meta-analysis of longitudinal studies. AIDS, 20(73).
Freeman, E. E., White, R. G., Bakker, R., Orroth, K. K., Weiss, A. H., Buv, A., Hayes, R. J., and Glynna, J. R. (2009). Population-level effect of potential HSV-2 prophylactic vaccines on HIV incidence in sub-saharan Africa. Vaccine, 27, 940-946.
Golin, C. E., Liu, H., Hays, R. D., Miller, L. G., Beck, C. K., Ickovics, J. A., Kaplan, H., and Wenger, N. S. (2002). A prospective study of predictors of adherence to combination antiretroviral medication. Journal of General Internal Medicine, 17(10).
Helton, J. C. (1993). Uncertainty and sensitive analysis techniques for use in performance assessments for radioactive waste disposal. Reliability Engineering and System Safety, 42, 327-367.
Lakshmikantham, V., Leela, S., and Martynyuk, A. A. (1989). Stability analysis of nonlinear systems. New York: Marcel Dekker, Inc.
Lenhart, S., and Workman, J. T. (2007). Optimal control applied to biological models. London: Chapman and Hall.
Magombedze, G., Garira, W., Mwenje, E., and Bhunu, C. P. (2011). Optimal control for HIV-1 triple therapy. International Journal of Computer Mathematics, 108, 314-340.
Mbopi-Keou, F. X., Gresenguet, G., Mayaud, P., Weiss, H. A., Gopal, R., and Marta, M. (2000). Interactions between herpes simplex virus type 2 and human immunodeficiency virus type 1 infection in African women: Opportunities for intervention. Journal of Infectious Diseases, 182(4).
McClelland, R. S., Wang, C., and Overbaugh, J. (2002). Association between cervical shedding of herpes simplex virus and HIV-1. AIDS, 16(18).
Mhlanga, A., Bhunu, C. P., and Mushayabasa, S. (2015). A computational study of HSV-2 with poor treatment adherence. Abstract and Applied Analysis, 8506, 1-15.
Mukandavire, Z., Gumel, A. B., Garira, W., and Tchuenche, J. M. (2009). Mathematical analysis of a model for HIV-malaria co-infection. Mathematical Biosciences and Engineering, 6(2).
Mushayabasa, S., Tchenche, J. M., Bhunu, C. P., and Ngarakana-Gwasira, E. (2011). Modelling gonorrhea and HIV co-interaction. Biosystems, 103, 27-37.
Owusu-Edusei, K. Jr., Chesson, H. W., Gift, T. L., Tao, G., Mahajan R., Ocfemia M. C., and Kent, K. C. (2008). The estimated direct medical cost of selected sexually transmitted infections in the United States. Transmitted Diseases, 40(3).
Plummer, M. L., Watson-Jones, D., Lees, S., Baisley, K., Matari, S., Changalucha, Clayton, J. T., Mugeye, K., and Tanton, C. (2010). Herpes suppressive therapy for HIV prevention on Yanzania. AIDS Care, 22(4).
Pontryagin, L. S. (1962). Mathematical theory of optimal processes. New York, London: Interscience Publishers John Wiley and Sons.
Reynolds, S. J., and Quinn, T. C. (2005). Developments in STD/HIV interactions and intertwining epidemics of HIV and HSV-2. Infectious Disease Clinics of North America, 19, 415-425.
Sharomi, O., and Gumel, A. B. (2007). Curtailing smoking dynamics: A mathematical modelling approach. Applied Mathematics and Computations, 195, 475-499.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 International Journal of Development Mathematics (IJDM)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors are solely responsible for obtaining permission to reproduce any copyrighted material contained in the manuscript as submitted. Any instance of possible prior publication in any form must be disclosed at the time the manuscript is submitted and a
copy or link to the publication must be provided.
The Journal articles are open access and are distributed under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs 4.0 IGO License, which permits use,
distribution, and reproduction in any medium, provided the original work is properly cited.
No modifications or commercial use of the articles are permitted.
