A GUMBORO-SALMONELLA CO-INFECTION MATHEMATICAL MODEL WITH OPTIMAL CONTROL
Keywords:
Gumboro, Salmonella, Optimal control, Numerical SimulationAbstract
Poultry production contributes immensely to the economic growth of a country. For instance in Kenya, 20
tonnes of poultry meat worth 3.5 billion kenya shillings and 1.3 billion eggs worth 9.7 billion Kenya Shillings
come from this sector. However, the sector is greatly threatened by poultry diseases among them, Gum-
boro(IBD) and Salmonella as inadequate knowledge exists of optimal control strategies for various poultry
co-infections. In this research, a Gumboro-Salmonella co-infection mathematical model with optimal control
is developed using a system of ODEs to perform an optimal control analysis. The analysis was done by for-
mulating an optimal control problem and using Pontryagin’s maximum principle to solve it. The Numerical
simulation results showed that the best Gumboro-Salmonella co-infection control strategy involved combining
all the interventions
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References
] Zootecnica intenational 2016. Poultry sector in Kenya. Retrived from
https://zootecnicainternational.com/field-reports/poultry-sector-kenya/ On 8/8/2021
Mengesha, M., and Tsega, W. (2011). Phenotypic and genotypic characteristics of indigenous chicken
in Ethiopia. African Journal of Agricultural Research Vol. 6(24), pp. 5398-5404, 26 October, 2011.
DOI:10.5897/AJAR11.434 I.
Kingori, A.M., Wachira, A.M ., Tuitoek, J.K.(2010). Indigenous chicken production in
kenya:Areview.international journal of poultry science v.9 pg309-316.Doi:10.3923/ijps.2010.309-316.
Nyaga, P. (2007) Strategies for prevention and control of infectious disease.Food and agricultural organization of the united nations.
George, T. and Jessica, B.W. (2018). Infectious bursal disease(GUMBORO )in backyard chicken. Mississippi state university publication number P3211.
Mutinda, W.U., Nyaga, P.N., Njagi, L.W., Bebora L.C., Mbuthia, P.G. (2018). Gumboro disease outbreaks
cause high mortality rates in indigenous chickens in kenya.Bulletin health and production Africa 61.571-
Marketing Kepro (2017) Salmonellosis in poultry. Retrived from
https://www.viv.net/articles/blog/salmonellosis-in-poultry on 23/6/2021
Liljebjelke, K.A, Hofacre, C.L., Liu, T., White, D.G., Ayers, S., Young, S., Maurer J.J. (2005). Vertical and
horizontal transmission of salmonella within integrated broiler production system. Foodborne Pathog
Dis. 2005 Spring;2(1):90-102. doi: 10.1089/fpd.2005.2.90. PMID: 15992303.
Mishra, B.K., Sinha, D.N. (2016). A Mathematical Model on Avian Infuenza with Quarantine and Vaccination. J Immunol Tech Infect Dis 5:4. doi: 10.4172/2329-9541.1000152
Omollo, A.E., and George, K.,(2020).Formulation of a Mathematical Model for the Transmission Dynamics of Infectious Bursal Disease (IBD), Incorporating Eects of Environmental Factors. Asian Research
Journal of Mathematics, Page 20-35. DOI: 10.9734/arjom/2020/v16i930217 Published: 21 August
Uwakwe, J.,Inyama, S.C.,Emerenini B.O.,Celestine A.N(2019) .A mathematical and control model of
Bursal disease (ibd). IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X.
Volume 15, Issue 4 Ser. III (Jul – Aug 2019), PP 15-29 www.iosrjournals.org
Daozhou G,Shigui R and Travis P (2016).Coinfection dynamics of two diseases in a single host population. Journal of Mathematical Analysis and Applications 442(1). DOI:10.1016/j.jmaa.2016.04.039
Shaibu, O., and Daniel, O.M.,(2018). A mathematical model for coinfection of listeriosis and antrax
diseases. International journal of mathematics and mathematics sciences.Vol. 2018 |Article ID 1725671
| https://doi.org/10.1155/2018/1725671
Lusiana, V., Nuraini, N. and Soewono, E. (2017) Mathematical modelling of transmission coinfection
dynamics of tuberculosis in HIV community. Indonesia
Musaili, J. S., Chepkwony, I., & Mutuku, W. N. (2024). Mathematical Modeling of the Transmission
Dynamics of Gumboro Disease. Journal of Applied Mathematics, 2024(1), 2514740.
Pontryagin, L. S., Boltyanskii, V. G., Gamrelidze, R. V., and Mishchenko, E. F. (1962). The Mathematical
Theory of Optimal Processes. John Wiley, New York
Prevost, K., Magal, P., & Beaumont, C. (2006). A model of Salmonella infection within industrial house
hens. Journal of Theoretical Biology, 242(3).
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Copyright (c) 1970 Jane Musaili, Dr. Isaac chepkwony, Dr. Winfred Mutuku
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