Document Type : Research Paper

Authors

Department of Mathematics, College of Natural and Computational Science, Wollega University, Nekemte, Ethiopia.

Abstract

The aim of study is to formulate and analyze a mathematical model for coinfection of sexually transmitted diseases HPV, HIV, and HSV-II. The well possedness of the developed model equations was proved and the equilibrium points of the model have been identified. Qualitative analysis of the formulated model equations was proved and the equilibrium points of the model have been identified. Qualitative analysis of the formulated model was established using basic reproduction number. The results show that the disease free equilibrium is locally asymptotically stable if the basic reproduction is less than one. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Finally, numerical simulations of the model equations are carried out using the software MATLAB R2015b with ODE45 solver. Numerical simulations illustrated that all infection solutions converge to zero when the basic reproduction number is less than unity.

Keywords

[1]      Shahzad, N., Farooq, R., Aslam, B., & Umer, M. (2017). Microbicides for the Prevention of HPV, HIV-1, and HSV-2: Sexually Transmitted Viral Infections. In Fundamentals of sexually transmitted infections.  DOI: 10.5772/intechopen.68927
[2]      Bergot, A. S., Kassianos, A., Frazer, I. H., & Mittal, D. (2011). New approaches to immunotherapy for HPV associated cancers. Cancers3(3), 3461-3495.
[3]      Lowy, D. R., & Schiller, J. T. (2006). Prophylactic human papillomavirus vaccines. The journal of clinical investigation116(5), 1167-1173.
[4]      World Health Organization. (2017). WHO list of priority medical devices for cancer management. World Health Organization.
[5]      Wodarz, D. (2007). Killer cell dynamics mathematical and computational approaches to immunology. Springer.
[6]      Nowak, M., & May, R. M. (2000). Virus dynamics: mathematical principles of immunology and virology: mathematical principles of immunology and virology. Oxford University Press, UK.
[7]      UNAIDS data 2019. (2019). Retrieved from https://www.unaids.org/en/resources/documents/2019/2019-UNAIDS-data
[8]      CDC. (2001). Genital herpes information.  Retrieved July 15, 2020, from www.cdc.gov/std/Herpes/default.htm
[9]       WHO guidelines for the treatment of genital herpes simplex virus. (2016). World Health Organization. Retrieved from  file:///C:/Users/jpour/Downloads/9789241549875-eng.pdf
[10]  Taira, A. V., Neukermans, C. P., & Sanders, G. D. (2004). Evaluating human papillomavirus vaccination programs. Emerging infectious diseases10(11), 1915-1923.
[11]  Ribassin-Majed, L., Lounes, R., & Clémençon, S. (2012). Efficacy of vaccination against HPV infections to prevent cervical cancer in France: present assessment and pathways to improve vaccination policies. PloS one7(3), e32251.
[12]  Gurmu, E. D., & Koya, P. R. (2019). Sensitivity analysis and modeling the impact of screening on the transmission dynamics of human papilloma virus (HPV). American journal of applied mathematics7(3), 70-79. Doi: 10.11648/j.ajam.20190703.11
[13]  Okosun, K. O., Makinde, O. D., & Takaidza, I. (2013). Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives. Applied mathematical modelling37(6), 3802-3820.
[14]  Silva, C. J., & Torres, D. F. (2017). Modeling and optimal control of HIV/AIDS prevention through PrEP. Discrete and continuous dynamical systems series S, 11(9), 119-141. 10.3934/dcdss.2018008
[15]  Gurmu, E. D., Bole, B. K., & Koya, P. R. (2020). Mathematical Modelling of HIV/AIDS Transmission Dynamics with Drug Resistance Compartment. American journal of applied mathematics8(1), 34-45.
[16]  Schiffer, J. T., Swan, D. A., Magaret, A., Schacker, T. W., Wald, A., & Corey, L. (2016). Mathematical modeling predicts that increased HSV-2 shedding in HIV-1 infected persons is due to poor immunologic control in ganglia and genital mucosa. PloS one11(6), e0155124. Doi:10.1371/journal.pone.0155124
[17] Mhlanga, A., Bhunu, C. P., & Mushayabasa, S. (2015, November). A computational study of HSV-2 with poor treatment adherence. Abstract and applied analysis (Vol. 2015). https://doi.org/10.1155/2015/850670
[18] Gurmu, E. D., Bole, B. K., & Koya, P. R. (2020). Mathematical model for co-infection of HPV with cervical cancer and HIV with AIDS diseases. Int. J. Sci. Res. in mathematical and statistical sciences, 7(2), 107-121.
[19] Sanga, G. G., Makinde, O. D., Massawe, E. S., & Namkinga, L. (2017). Modeling co-dynamics of Cervical cancer and HIV diseases. Global journal of pure and applied mathematics13(6), 2057-2078.
[20] Gurmu, E. D., Bole, B. K., & Koya, P. R. (2020). A Mathematical model for co-infection of HPV and HSV-II with drug resistance compartment. Int. J. Sci. Res. in mathematical and statistical sciences, 7(2), 34-46.
[21] Hühns, M., Simm, G., Erbersdobler, A., & Zimpfer, A. (2015). HPV infection, but not EBV or HHV-8 infection, is associated with salivary gland tumours. BioMed research international. https://doi.org/10.1155/2015/829349
[22] Mhlanga, A. (2018). A theoretical model for the transmission dynamics of HIV/HSV-2 co-infection in the presence of poor HSV-2 treatment adherence. Applied mathematics and nonlinear sciences3(2), 603-626.
[23] Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences180(1-2), 29-48.
[24] Weinstein, S. J., Holland, M. S., Rogers, K. E., & Barlow, N. S. (2020). Analytic solution of the SEIR epidemic model via asymptotic approximant. Physica D: nonlinear phenomena411, 132633. https://doi.org/10.1016/j.physd.2020.132633