Applied and Computational Mathematics
Volume 9, Issue 3, June 2020, Pages: 70-84
Received: Dec. 9, 2019;
Accepted: Jan. 10, 2020;
Published: Jun. 4, 2020
Views 193 Downloads 129
Uwakwe Joy Ijeoma, Department of Mathematics, Alvan Ikoku Federal College of Education, Owerri, Nigeria
Inyama Simeon Chioma, Department of Mathematics, Federal University of Technology, Owerri, Nigeria
Omame Andrew, Department of Mathematics, Federal University of Technology, Owerri, Nigeria
We formulated a five compartmental model of ND for both the ordinary and control models. We first determined the basic Reproduction number and the existence of Steady (Equilibrium) states (disease-free and endemic). Conditions for the local stability of the disease-free and endemic steady states were determined. Further, the Global stability of the disease-free equilibrium (DFE) and endemic equilibrium were proved using Lyponav method. We went further to carry out the sensitivity analysis or parametric dependence on R0 and later formulated the optimal control problem. We finally looked at numerical Results on poultry productivity in the presence of Infectious Newcastle Disease (ND) and we drew six graphs to demonstrate this. We observe that in absence of any control measure, the number of latently infected birds will increase rapidly from the initial population size of 80 to 160 birds within 1-3 days, whereas in the presence of control measures the population size will reduces to about 30 birds and goes to a stable state. This shows that the control measures are effective. The effect of the three control measures on the infectious classes can be seen. The number of non-productive infectious birds reduces to zero with control whereas the number of infectious productive reduces to about 8 birds and goes to its stable state when control is applied. This shows that the application of all three control measures tends to be more effective in the non- productive infectious bird population. It was also establish that the combination of efficient vaccination therapy and optimal efficacy of the vaccines are significantly more effective in the infectious productive birds’ population, since the combination reduces the population size of the birds to zero with 9–10 days. From the simulation also we see that optimal efficacy of the vaccine and effort to increase the number of recovered birds increases the number of latently infected birds population to about 129 at the early days of the infection whereas from another graph, the infectious productive birds reduces to 15 while the non -productive birds reduces to zero. The results from the simulation also show clearly, the effect of vaccination therapy on the latently infected birds. We observe that this programme will reduce the number of latently infected birds even if it not done more often. From the simulation, we further observe that this programme has effect on the infectious classes especially the non-productive infectious bird population, which reduces to zero after about 4 days.
Uwakwe Joy Ijeoma,
Inyama Simeon Chioma,
Mathematical Model and Optimal Control of New-Castle Disease (ND), Applied and Computational Mathematics.
Vol. 9, No. 3,
2020, pp. 70-84.
Achoja, F. O., Ike, P. C., Akporhuarcho, P. O. (2010). Economics of Veterinary Services delivery among commercial poultry farmers in a market–driven economy: Evidence from Delta state, Nigeria. International Journal of Poultry Science 9, 1140-1145.
Alabi, R. A., Tariuma, I. O., Onemolense, P. E. A., Mafimisebi, A., Isah, T. A., Esobhawa, A. O., Oviasogie, D. I. (2000). Risk management in poultry enterprises in Edo state insurance scheme proceedings of the 5th Annual conference of Animal Science Association of Nigeria, Sept. 19-22, Portharcourt. pp 182-184.
Alders, R. G., Bagnol, B., Costa, R. & Young, M. P. (2012). Sustainable control of Newcastle Disease in village poultry. INFPD International Network for Family Poultry Development (FAO) GPFRP Note No. 05.
Blake, D. P., Tomley F. M., (2014) Securing Poultry Production from the ever–present Eimeria Challenge; Trends in Parasitology, 30 (1): 12–19.
Bowong, S., Alaoui, A. (2013) Optimal intervention strategies for tuberculosis; Communications in Nonlinear science and Numerical simulations, 18 (6), 1441–1453.
Buonomo, B., Lotignola D., Vargas De-Leon, C. (2014) Qualitative analysis and optimal control of an epidemic model with vaccination and treatment; Mathematics and Computers in Simulation, 100 pp 88–102.
Cassidy, L. R., Calistus, N. N. & Mathew, H. B. (2015). Modelling the burden of poultry disease on the rural poor in Madagascar. Elsevier One Health, 1 (6065).
Docherty, D. E., Friend M. (1999). Newcastle Disease. General Field procedures and diseases of Birds; Madison, Wis, USA: USGS–National Wildlife Health Center, pp 175-180.
Dortmans, J. C., Peeters B. P., Koch G. (2012). Newcastle disease virus outbreaks: vaccine mismatch or inadequate application? Veterinary Microbiology 160 (1-2): 17-22. Doi: 10.1016/.j.vetmic.2012-05.003.
Dortmans, J. C., Peeters, B. P., Koch, G. (2014). Field vaccinated chickens with low antibody titres, Showing equally insufficient protection against matching and non-matching genotypes of Virulent Newcastle disease virus; Veterinary Microbiology, 172 (1-2), 100-107; doi: 10.1016/j.vetmic.2014.05.004.
Newcastle disease transmission and illegal trade on a wild population of white–winged parakeetsin Peru: A modelling approach. PLoS ONE 11 (1): e0147517. doi: 10.1371/journal.pone.0147517.
Fangge, L., Peixian, L. (2011). ARMA model for predicting the number of new outbreaks of Newcastle disease during the month. Computer Science & Automation Engineering (CSAE) 2011 IEEE International Conference. Doi: 10.1109/CSAE.2011.5952933.
Fox, W. (2010). Tick–borne disease–risks and reality, Borreliosis and Associated disease Awareness UK 2010.
Harrison, E. M. (2013). Epidemiology and evolution of vector borne disease. Department of Mathematical sciences, University of Bath.
Hugo, A., Makinde, O. D., Karmar, S., Chibwana F. (2016). Optimal control and cost effectiveness analysis for Newcastle disease eco–epidemiological model in Tanzania. Journal of Biological dynamics Vol. 11, No 1, 190-209.
Ibu, O. J., Adulugba A., Adeleke M. A., Tijjani A. Y. (2000). Activity of Newcastle disease and Infectious bursal disease viruses in ducks and guinea fowls in Jos area, Nigeria. Journal of Veterinary Sciences, vol. 2, pp 45-46.
Jake, M. F., Jessia B. L., Vincent L. C., Andres J. G., Elizabeth A. H., Maia M., Craig, W. O. (2014). Optimal sampling strategies for detecting Zoonotic disease epidemics; (Article on maternal Health task force year 5); Available online at http://dx.doi.org/10.1371/journal.pibi.1003668.
Jing, L., Xu D., Zang J., Xiao J., Wang H. (2010). The comparison of ARMA exponential Smoothing and seasonal Index model for predicting incidence of Newcastle Disease; World Automation Congress (WAC).
Jos, C. F. M., Dortmas J. C., Koch G., Rottier P. J. M., Peters B. P. H. (2011). Virulence of Newcastle Disease virus: What is known so far? Veterinary Research 42: 122. doi: 10.1186/1297-9716, 42-122.
Kapczynski, D. R., Afonso, C. L., Miller, P. J. (2013). Immune response to poultry to Newcastle disease virus. Dev. Comp. Immunology 41 (3): 447-533. doi: 10.1016/j.dci.2013.04.012.
Karl, M. R. (2007). New methods for integrated models of animal disease control. Selected paper prepared for the 2007 American Agricultural Economics Association meetings, Portland.
Linda, P. H. (2009). Epidemiology and characterization of Newcastle disease in small holder poultry in Mozambique; Available online at http:/epsilon.slu.se, ISSN 1652-8697.
Ologbon, O. A. C., Ambatu O. I. (2012). Poultry enterprise combination among small–scale farmers in Ogun state, Nigeria: A technical sufficiency approach. Journal of Agricultural Veterinary Science, 4: 7-15.
Oluwayelu, D. O., Adeiyi A. I., Olaniyian I., Ezewele P., Oluwasanmi A. (2014). Occurrence of Newcastle disease and infectious bursal disease virus antibodies in double–spurred Francolins of Nigeria; Journal of veterinary medicine 106898. Doi: 10.1155/2014/106898.
Omame, A., Okuonghae, D., Umana, R. A., Inyama, S. C., (2020). Analysis of a co-infection model for HPV-TB, Applied Mathematical Modelling, 77: 881-901
Senne, D. A., King, D. J., Kapczynski D. R. (2004). Control of Newcastle disease by vaccination. Dev. Biology (Basel), 119: 165-170.
Sharma, S., Samanta G. P. (2015). Stability analysis and optimal control of an epidemic model with vaccination. International Journal of Biomathematics, vol. 8, issue 03.
Udofia, Ekere Sunday and Inyama, Simeon Chioma (2011) Mathematical Modeling of the Transmission Dynamics of Fowl Pox in Poultry, Journal of Modern Mathematics and Statistics 5 (5-6), Pp 106-111.
Udofia, Ekere Sunday and Inyama, Simeon Chioma (2012) Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry, Journal of Mathematics and Statistics 8 (2), Pp. 248-2012.
Van, B. M., Bouwa A., Fabri T. H., Katsma E., Hartog L., Koch G. (2008). Herd immunity to Newcastle disease virus in poultry by vaccination. Journal of Avian Pathology 37 (1): 1-5. doi: 10.1080/03079450701772391.