All Title Author
Keywords Abstract


Modeling the Transmission Dynamics of the Monkeypox Virus Infection with Treatment and Vaccination Interventions

DOI: 10.4236/jamp.2017.512191, PP. 2335-2353

Keywords: Basic Reproduction Number, Comparison Theorem, Equilibria, Monkeypox, Sensitivity Analysis, Stability Analysis

Full-Text   Cite this paper   Add to My Lib

Abstract:

Presently, an ongoing outbreak of the monkeypox virus infection that began in Bayelsa State of Nigeria has now spread to other parts of the country including mostly States in the South-South with the Nigerian Ministry of Health confirming 4 samples out of the 43 sent for testing at WHO Regional Laboratory in Dakar, Senegal. This reminds us that apart from the eradicated smallpox, there are other poxviruses that pose potential threat to people in West and Central Africa. In this paper, we developed a mathematical model for the dynamics of the transmission of monkeypox virus infection with control strategies of combined vaccine and treatment interventions. Using standard approaches, we established two equilibria for the model namely: disease-free and endemic. The disease-free equilibrium was proved to be both locally and globally asymptotically stable if R0 < 1 using the next-generation matrix and the comparison theorem. While the endemic equilibrium point existed only when R0 > 1, was proved to be locally asymptotically stable if R0 > 1 using the linearization plus row-reduction method. The basic reproduction numbers for the humans and the non-human primates of the model are computed using parameter values to be R0,h = 9.1304 x 10-6 and R0,n = 3.375 x 10-3 respectively. Numerical simulations carried out on the model revealed that the infectious individuals in the human and non-human primates’ populations will die out in the course of the proposed interventions in this paper during the time of the study. Sensitivity analysis carried out on the model parameters shows that the basic reproduction numbers of the model which served as a threshold for measuring new infections in the host populations decrease with increase in the control parameters of vaccination and treatment.

References

[1]  CDC (2003) Update: Multistate Outbreak of Monkeypox—Illinois, Indiana, Kansas, Missouri, Ohio and Wisconsin.
https://www.cdc.gov/mmwr/preview/mmwrhtml/mm5227a5.htm
[2]  Jezek, Z., Szczeniowski, M., Paluku, K.M., Mutombo, M. and Grab, B. (1988) Human Monkeypox: Confusion with Chickenpox. Acta Tropica, 45, 297-307.
[3]  Ladnyj, I.D., Ziegler, P. and Kima, E. (1972) A Human Infection Caused by Monkeypox Virus in Basankusu Territory, Democratic Republic of Congo. Bulletin of the World Health Organization, 46, 593-597.
[4]  Von Magnus, P., Andersen, E.K., Petersen, K.B. and Birch-Anderson, A.A. (1959) A Pox-Like Disease in Cynomolgus Monkeys. Acta Pathol Microbiol Immunol Scand, 46, 156-176.
https://doi.org/10.1111/j.1699-0463.1959.tb00328.x
[5]  CDC (2003) What You Should Know about Monkeypox.
https://www.cdc.gov/poxvirus/monkeypox/
[6]  Sola, O. (2017) NCDC Confirms 12 Suspected Monkeypox Cases in Bayelsa. Vanguard Online Newspaper.
[7]  The Eagle Online (2017) Breaking: FG Confirms Only Four Cases.
https://theeagleonline.com.ng/breaking-monkey-pox-fg-confirms-only-four-cases/
[8]  World Health Organization (WHO) (1999) Technical Advisory Group on Human Monkeypox Report of a WHO Meeting. WHO, Geneva.
http://www.who.int/emc
[9]  Bhunu, C.P. and Mushayabasa, S. (2011) Modeling the Transmission Dynamics of Pox-Like Infections. International Journal of Applied Mathematics, 41, 2.
[10]  Niwas, L. (3003) Mathematical Modeling of Smallpox with Optimal Intervention Policy. Master’s Thesis, University of Central Florida, Orlando.
[11]  Babak, P., Lauren, A.M., Danuta, M.S., Mel, K., David, M.P. and Robert, C.B. (2005) Modeling Control Strategies of Respiratory Pathogens. Emerging Infectious Diseases, 11, 1249-1256.
http://www.cdc.gov/eid
[12]  Birkhof, G. and Rota, G.C. (1989) Ordinary Differential Equations. MIT Press, Boston.
[13]  Van den Driessche, P. and Watmough, J. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180, 29-48.
https://doi.org/10.1016/S0025-5564(02)00108-6
[14]  Diekmann, O., Heesterbeek, J.A. and Metz, J.A.J. (1990) On the Definition and the Computation of the Basic Reproductive Ratio, R0 in Models of Infectious Diseases in Heterogeneous Populations. Journal of Mathematical Biology, 28, 365-382.
https://doi.org/10.1007/BF00178324
[15]  Usman, S., Adamu, I.I. and Aliyu, H.B. (2017) Mathematical Model for the Transmission Dynamics of Zika Virus Infection with Combined Vaccination and Treatment Interventions. Journal of Applied Mathematics and Physics, 5, 1964-1978.
[16]  Usman, S., Adamu, I.I. and Dahiru, U. (2017) Stability Analysis of a Mathematical Model for the Transmission Dynamics of Zika Virus Infection. Journal of the Nigerian Association of Mathematical Physics, 40.
https://www.researchgate.net/publication/320617743
[17]  Shaban, N. and Hawa, M. (2014) Modeling the Impact of Vaccination and Screening on the Dynamics of Human Papillomavirus Infection. International Journal of Mathematical Analysis, 8, 441-454.
http://dx.doi.org/10.12988/ijma.2014.312302
https://doi.org/10.12988/ijma.2014.312302
[18]  Chitnis, N., Hyman, J.M. and Cushing, J.M. (2008) Determining Important Parameters in the Spread of Malaria through the Sensitivity Analysis of a Mathematical Model. Bulletin of Mathematical Biology, 70, 1272.
https://doi.org/10.1007/s11538-008-9299-0

Full-Text

comments powered by Disqus