Mathematical modelling for the transmission dynamics of Rift Valley fever virus with human host

Festus Abiodun Oguntolu, Deborah W. Yavalah, Collins F. Udom, Olumuyiwa James Peter, Kayode Oshinubi

Abstract


Rift Valley Fever (RVF) is a viral zoonosis spread primarily by mosquitos that primarily affects livestock but has the potential to affect humans. Because of its potential to spread quickly and become an epidemic, it has become a public concern. In this article, the transmission dynamics of RVF with mosquito, livestock and human host using a compartmental model is studied and analyzed. The basic reproduction number R0 is computed using next generation matrix and the disease-free equilibrium state is found to be locally asymptotically stable if R0 < 1 which implies that rift valley fever could be put under control in a population where the reproduction number is less than 1. The numerical simulations give insightful results to further explore the dynamics of the disease based on the effect of three interventions; efficacy of vaccination, culling of livestock and trapping of mosquitoes introduced in the model.

Keywords


Rift valley Fever; Human host; Transmission Dynamics; Mathematical Modeling

Full Text:

PDF

References


A. A. Adeyeye, P. S. Ekong, N. N. Pilau et al., “Rift valley fever: the nigerian story,” Veterinaria Italiana, vol. 47, no. 1, pp. 35–40, 2011.

A. Evans, F. Gakuya, J. T. Paweska, M. Rostal, L. Akoolo, P. J. Van Vuren, T. manyibe, J. M. Macharia, T. G. Ksiazek, D. R. Feikin, R. F. Breiman, and M. Kariuki Njenga, “Prevalence of antibodies against Rift Valley fever virus in Kenyan wildlife,” Epidemiology and Infection, vol. 136, no. 9, pp. 1261–1269, 2008. DOI: 10.1017/S0950268807009806

Y. B. Kanouté, B. G. Gragnon, C. Schindler, B. Bonfoh, and E. Schelling, “Epidemiology of brucellosis, Q Fever and Rift Valley Fever at the human and livestock interface in northern Côte d’Ivoire,” Acta Tropica, vol. 165, pp. 66–75, 2017. DOI: 10.1016/j.actatropica.2016.02.012

W. H. O. (WHO), Information on Rift Valley Fever . WHO, 2018. [Online]. Available: www.who.int/emergencies/diseases/rift-valley-fever

O. James Peter, R. Viriyapong, F. A. Oguntolu, P. Yosyingyong, H. O. Edogbanya, and M. O. Ajisope, “Stability and optimal control analysis of an SCIR epidemic model,” Journal of Mathematical and Computational Science, vol. 10, no. 6, pp. 2722–2753, 2020. DOI: 10.28919/jmcs/5001

O. J. Peter, S. Kumar, N. Kumari, F. A. Oguntolu, K. Oshinubi, and R. Musa, “Transmission dynamics of Monkeypox virus: a mathematical modelling approach,” Modeling Earth Systems and Environment, 2021. DOI: 10.1007/s40808-021-01313-2

O. J. Peter, S. Qureshi, A. Yusuf, M. Al-Shomrani, and A. A. Idowu, “A new mathematical model of COVID-19 using real data from Pakistan,” Results in Physics, vol. 24, p. 104098, 2021. DOI: 10.1016/j.rinp.2021.104098

A. Abioye, M. Ibrahim, O. Peter, S. Amadiegwu, and F. Oguntolu, “Differential transform method for solving mathematical model of seir and sei spread of malaria,” International Journal of Sciences: Basic and Applied Research, vol. 40, no. 1, pp. 197–219, 2018.

A. I. Abioye, O. J. Peter, H. A. Ogunseye, F. A. Oguntolu, K. Oshinubi, A. A. Ibrahim, and I. Khan, “Mathematical model of COVID-19 in Nigeria with optimal control,” Results in Physics, vol. 28, p. 104598, 2021. DOI: 10.1016/j.rinp.2021.104598

T. A. Ayoola, H. O. Edogbanya, O. J. Peter, F. A. Oguntolu, K. Oshinubi, and M. L. Olaosebikan, “Modelling and optimal control analysis of typhoid fever,” Journal of Mathematical and Computational Science, vol. 11, no. 6, pp. 6666–6682, 2021. DOI: 10.28919/jmcs/6262

O. Peter, M. Ibrahim, F. Oguntolu, O. Akinduko, and S. Akinyemi, “Direct and indirect transmission dynamics of typhoid fever model by differential transform method,” ATBU, Journal of Science, Technology & Education, vol. 6, no. 1, pp. 167–177, 2018.

O. J. Peter, A. S. Shaikh, M. O. Ibrahim, K. Sooppy Nisar, D. Baleanu, I. Khan, and A. I. Abioye, “Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator,” Computers, Materials & Continua, vol. 66, no. 2, pp. 1823–1848, 2021. DOI: 10.32604/cmc.2020.012314

Q. Mehmood, M. Irfan, I. O. Ogunkola, F. Jaguga, and I. Ullah, “Rift valley fever and covid-19 outbreak in kenya: a double whammy,” Ethics, Medicine, and Public Health, vol. 19, p. 100685, 2021. DOI: 10.1016/j.jemep.2021.100685

O. Uwishema, E. Chalhoub, T. Torbati, S. C. David, C. Khoury, L. L. P. A. Ribeiro, Y. Nasrallah, B. K. Bekele, and H. Onyeaka, “Rift Valley fever during the COVID–19 pandemic in Africa: A double burden for Africa’s healthcare system,” Health Science Reports, vol. 5, no. 1, 2022. DOI: 10.1002/hsr2.468

S. S. Nielsen et al., “Scientific Opinion on the assessment of the control measures of the category A diseases of Animal Health Law: Highly Pathogenic Avian Influenza,” EFSA Journal, vol. 19, no. 1, 2021. DOI: 10.2903/j.efsa.2021.6372

R. Métras, W. J. et al.Edmunds, C. Youssouffi, L. Dommergues, G. Fournié, A. Camacho, S. Funk, E. Cardinale, G. Le Godais, S. Combo, L. Filleul, H. Youssouf, and M. Subiros, “Estimation of Rift Valley fever virus spillover to humans during the Mayotte 2018–2019 epidemic,” Proceedings of the National Academy of Sciences, vol. 117, no. 39, pp. 24 567–24 574, 2020. DOI: 10.1073/pnas.2004468117

R. Métras, G. Fournié, L. Dommergues, A. Camacho, L. Cavalerie, P. Mérot, M. J. Keeling, C. Cêtre-Sossah, E. Cardinale, and W. J. Edmunds, “Drivers for Rift Valley fever emergence in Mayotte: A Bayesian modelling approach,” PLOS Neglected Tropical Diseases, vol. 11, no. 7, p. e0005767, 2017. DOI: 10.1371/journal.pntd.0005767

M. Fawzy and Y. A. Helmy, “The One Health Approach is Necessary for the Control of Rift Valley Fever Infections in Egypt: A Comprehensive Review,” Viruses, vol. 11, no. 2, p. 139, 2019. DOI: 10.3390/v11020139

J. M. Gachohi, M. K. Njenga, P. Kitala, and B. Bett, “Modelling Vaccination Strategies against Rift Valley Fever in Livestock in Kenya,” PLOS Neglected Tropical Diseases, vol. 10, no. 12, p. e0005049, 2016. DOI: 10.1371/journal.pntd.0005049

F. Chamchod, C. Cosner, R. S. Cantrell, J. C. Beier, and S. Ruan, “Transmission Dynamics of Rift Valley Fever Virus: Effects of Live and Killed Vaccines on Epizootic Outbreaks and Enzootic Maintenance,” Frontiers in Microbiology, vol. 6, p. 1568, 2016. DOI: 10.3389/fmicb.2015.01568

S. C. Mpeshe, H. Haario, and J. M. Tchuenche, “A Mathematical Model of Rift Valley Fever with Human Host,” Acta Biotheoretica, vol. 59, no. 3-4, pp. 231–250, 2011. DOI: 10.1007/s10441-011-9132-2

G. Lo Iacono, A. A. Cunningham, B. Bett, D. Grace, D. W. Redding, and J. L. N. Wood, “Environmental limits of Rift Valley fever revealed using ecoepidemiological mechanistic models,” Proceedings of the National Academy of Sciences, vol. 115, no. 31, pp. E7448–E7456, 2018. DOI: 10.1073/pnas.1803264115

Y. Xiao, J. C. Beier, R. S. Cantrell, C. Cosner, D. L. DeAngelis, and S. Ruan, “Modelling the Effects of Seasonality and Socioeconomic Impact on the Transmission of Rift Valley Fever Virus,” PLoS Neglected Tropical Diseases, vol. 9, no. 1, p. e3388, 2015. DOI: 10.1371/journal.pntd.0003388

S. C. Mpeshe, L. S. Luboobi, and Y. Nkansah-Gyekye, “Modeling the Impact of Climate Change on the Dynamics of Rift Valley Fever,” Computational and Mathematical Methods in Medicine, vol. 2014, pp. 1-12, 2014. DOI: 10.1155/2014/627586

E. A. Fischer, G.-J. Boender, G. Nodelijk, A. A. de Koeijer, and H. J. van Roermund, “The transmission potential of Rift Valley fever virus among livestock in the Netherlands: a modelling study,” Veterinary Research, vol. 44, no. 1, p. 58, 2013. DOI: 10.1186/1297-9716-44-58

W. S. D. Tennant, E. Cardinale, C. Cêtre-Sossah, Y. Moutroifi, G. Le Godais, D. Colombi, S. E. F. Spencer, M. J. Tildesley, M. J. Keeling, O. Charafouddine, V. Colizza, W. J. Edmunds, and R. Métras, “Modelling the persistence and control of Rift Valley fever virus in a spatially heterogeneous landscape,” Nature Communications, vol. 12, no. 1, p. 5593, 2021. DOI: 10.1038/s41467-021-25833-8

N. Chitnis, J. M. Hyman, and C. A. Manore, “Modelling vertical transmission in vector-borne diseases with applications to Rift Valley fever,” Journal of Biological Dynamics, vol. 7, no. 1, pp. 11–40, 2013. DOI: 10.1080/17513758.2012.733427

S. A. Pedro, S. Abelman, F. T. Ndjomatchoua, R. Sang, and H. E. Z. Tonnang, “Stability, Bifurcation and Chaos Analysis of Vector-Borne Disease Model with Application to Rift Valley Fever,” PLoS ONE, vol. 9, no. 10, p. e108172, 2014. DOI: 10.1371/journal.pone.0108172

S. A. Pedro, S. Abelman, and H. E. Z. Tonnang, “Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model,” PLOS Neglected Tropical Diseases, vol. 10, no. 12, p. e0005167, 2016. DOI: 10.1371/journal.pntd.0005167

O. Diekmann and J. A. P. Heesterbeek, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. John Wiley & Sons, 2000, vol. 5.

A. A. Majok, K. H. Zessin, M. P. O. Baumann, and T. B. Farver, “Analyses of baseline survey data on rinderpest in bahr el ghazal province, with proposal of an improved vaccination strategy against rinderpest for southern Sudan,” Tropical Animal Health and Production, vol. 23, no. 3, pp. 186–196, 1991. DOI: 10.1016/10.1007/BF02357004

O. James Peter, M. M. Ojo, R. Viriyapong, and F. Abiodun Oguntolu, “Mathematical model of measles transmission dynamics using real data from Nigeria,” Journal of Difference Equations and Applications, vol. 28, no. 6, pp. 753–770, 2022. DOI: 10.1080/10236198.2022.2079411

M. M. Ojo, O. J. Peter, E. F. D. Goufo, H. S. Panigoro, and F. A. Oguntolu, “Mathematical model for control of tuberculosis epidemiology,” Journal of Applied Mathematics and Computing, vol. 87, no. 5, pp. 707–718, 2022. DOI: 10.1007/s12190-022-01734-x




DOI: https://doi.org/10.34312/jjbm.v3i1.14160

Copyright (c) 2022 Festus Abiodun Oguntolu, Deborah W. Yavalah, Collins F. Udom, Olumuyiwa James Peter, Kayode Oshinubi

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:

                          EDITORIAL OFFICE OF JAMBURA JOURNAL OF BIOMATHEMATICS

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: editorial.jjbm@ung.ac.id
 +6281356190818 (Call/SMS/WA)
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.