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Bifurcation Analysis of Newcastle Disease Eco-epidemiological Model in the Presence of Vaccination: A Case of the Backyard Chicken
Journal of Humanities & Social Science (JHSS),
Vol. 9 No. 2 (2020): SPECIAL ISSUE OF SCIENCE, 2020
Abstract
Newcastle is an infectious disease caused by the avian paramyxomovirus-1. It occurs
most frequently as a disease of Avians (e.g., chicken, ducks, pigeons, guinea fowls and
other wild birds) that acquire viruses from infected Avians or a contaminated
environment. In this paper, we present a deterministic eco-epidemiological model for
Newcastle disease transmission in backyard chicken population in the presence of
vaccination as a control measure to study the nature of the equilibrium points. The
analytical and numerical methods were rigorously presented. Mathematical analysis of
the equilibrium point revealed that the model exhibits forward bifurcation. The analysis
show that a disease-free equilibrium point is locally asymptotically stable for effective
reproduction number ???????? < 1, and unstable when ???????? > 1. On the other hand, the
endemic equilibrium point is stable when ???????? < 1, and unstable otherwise. Furthermore,
the study revealed that increasing the vaccination rate leads to an increase in protective
immunity against Newcastle disease, and hence reduces the devastating effect of the
disease in a chicken population. The paper advises that stakeholders in backyard
chicken growers invest on intervention that ensures that effective reproduction number
is below a unit for successful control of the Newcastle disease.
Keywords
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- Alders, R., P. Spradbrow & M. Young. 2009. Village Chickens, Poverty Alleviation and the
- Sustainable Control of Newcastle Disease. Proceedings of An International Conference Held in Dar
- Es Salaam, Tanzania, 5–7 October 2005. ACIAR Proceedings No 131, 235.
- Alexander, D. J., J. G. Bell & R. G. Alders. 2004. FAO Technology Review: Newcastle Disease With
- Special Emphasis on Its Effect on Village Chickens. FAO Animal Production and Health, 4(ISSN
- –6019): 55.
- Alexander, D. J., R. J. Manvell, J. P. Lowings, K. M. Frost, M. S. Collins, P. H. Russell & J. E. Smith,1997.
- Antigenic Diversity and Similarities Detected in Avian Paramyxovirus Type 1 (Newcastle Disease
- Virus) Isolates Using Monoclonal Antibodies. Avian Pathology, 26(2): 399–418.
- Bhunu, C. P., W. Garira & Z. Mukandavire. 2009. Modeling HIV / AIDS and Tuberculosis Coinfection.
- Bulletin of Mathematical Biology, 71, 1745–1780.
- Brown, V. R. & S. N. Bevins. 2017. A Review of Virulent Newcastle Disease Viruses in the United
- States and the Role of Wild Birds in Viral Persistence and Spread. Veterinary Research, 48(1): 1–
- https://doi.org/10.1186/S13567-017-0475-9.
- Buonomo, B. & C. Vargas-De-León. 2013. Mathematical Biosciences Stability and Bifurcation
- Analysis of a Vector-Bias Model of Malaria Transmission. Mathematical Biosciences, 242(1): 59–
- https://doi.org/10.1016/J.Mbs.2012.12.001.
- Castillo-Chavez, C. 2004. Dynamical Models of Tuberculosis and Their Applications. Mathematical
- Biosciences and Engineering, 1(2): 361–404.
- Chingonikaya, E. E. & F. S. Salehe. 2018. Contribution of Local Chicken Production Towards
- Improving Peoples Wellbeing : a Case of Peri-Urban Areas of Kinondoni District , Tanzania. Asian
- Journal of Advances in Agricultural Research, 5(2): 1–11.
- Chuma, F., G. G. Mwanga & V. G. Masanja. 2019. Application of Optimal Control Theory To
- Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds As Reservoir of
- Disease Virus. Journal of Applied Mathematics. 2019. https://doi.org/10.1155/2019/3024965.
- Chuma, F., G. Mwanga & G. Kajunguri. 2018. Modeling the Role of Wild Birds and Environment in
- the Dynamics of Newcastle Diseasein Village Chicken. Asian Journal of Mathematics and
- Applications. 2018(November): 23.
- Daut, E. F., G. Lahodny, M. J. Peterson & R. Ivanek. 2016. Interacting Effects of Newcastle Disease
- Transmission and Illegal Trade on a Wild Population of White-Winged Parakeets in Peru: a
- Modeling Approach. Plos ONE, 11(1): 1–29. https://doi.org/10.1371/Journal.Pone.0147517.
- Dortmans, J. C., G. Koch, P. J. Rottier & B. P. Peeters. 2011. Virulence of Newcastle Disease Virus: What
- Is Known So Far? Veterinary Research, 42(1): 1–11. https://doi.org/10.1186/1297-9716-42-122.
- Driessche, P. Van Den & J. Watmough. 2002. Reproduction Numbers and Sub-Threshold Endemic
- Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180: 29–48.
- Edmund, J .R & V. Mwenda. 2018. Poultry Subsector in Tanzania: a Quick Scan. Embassy of the
- Kingdom of the Netherlands.
- Foppa, I. M. 2015. The Basic Reproductive Number of Tick-Borne Encephalitis Virus: An Empirical
- Approach. Journal of Mathematical Biology, January 2006, 13. https://doi.org/10.1007/S00285-005-
- -3.
- Hartemink, N. A., Randolph, S. E., Davis, S. A. & Heesterbeek, J. A. P. 2008. The Basic Reproduction
- Number for Complex Disease Systems : Defining R 0 for Tick-Borne Infections. JSTOR, 171(6):
- -754. https://doi.org/10.1086/587530.
- Hossain, M., M. Islam, M. Bari, M. Torab & M. Mondal. 2013. Seroprevalence of Newcastle Disease
- Virus in Backyard Chickens At Gazipur District of Bangladesh. International Journal of Natural
- Sciences, 3(1–4): 22–25.
- Hugo, A., O. D. Makinde, S. Kumar & F. F. Chibwana. 2017. Optimal Control and Cost Effectiveness
- Analysis for Newcastle Disease Eco-Epidemiological Model in Tanzania. Journal of Biological
- Dynamics, 11(1),190–209. https://doi.org/10.1080/17513758.2016.1258093.
- Kelatlhegile, G. R. & M. Kgosimore. 2016. Bifurcation Analysis of Vertical Transmission Model With
- Preventive Strategy. 0, 492–498. https://doi.org/10.1016/J.Joems.2015.10.001
- Lucchetti, J., M. Roy & M. Martcheva. 2009. An Avian Influenza Model and Its Fit To Human Avian
- Influenza Cases. Advances in Disease Epidemiology, 1, 1–30.
- Mafuta, P., J. Mushanyu, S. Mushayabasa & C. Bhunu. 2013. ’Transmission Dynamics of
- Trichomoniasis in Bisexuals’ Without the 'E' Transmission Dynamics of Trichomoniasis in
- Bisexuals ’ Without the ‘ E .’ World Journal of Modelling and Simulation, 9(4), 302–320.
- Mcdermott, J., P. Coleman & T. Randolph. 2000. Methods for Assessing the Impact of Infectious Diseases
- of Livestock - Their Role in Improving the Control of Newcastle Disease in Southern Africa. Aciar.
- Mengesha, M. 2012. Indigeneous Chicken Production and the Innate Characteristics. Asian Journal
- of Poultry Science, 6(2): 56–64.
- Michael, S., J. Stapleton & B. I. Shapiro. 2017. Tanzania Livestock Master Plan: Key Findings. ILRI
- Internal Report, Brief 1 Oc(Nairobi, Kenya), 1-4.
- Mlozi, M. R. S., A.V.M. Kakengi, U. M. Minga, A. M. Mtambo & J. E. Olsen. 2003. Marketing of Free
- Range Local Chickens in Morogoro and Kilosa Urban Markets, Tanzania. Livestock Research for
- Rural Development, 15(14).
- Munir, M. T. & M. R. Chowdhury. 2016. Emergence of New Sub-Genotypes of Newcastle Disease
- Virus in Pakistan. J Avian Res, 2(1): 1–7.
- Nyerere, N. & L. S. Luboobi. 2014. Bifurcation and Stability Analysis of the Dynamics of Tuberculosis
- Model Incorporating, Vaccination, Screening and Treatment. Commun. Math. Biol. Neurosci.
- Oluwayelu, D. O., A. I. Adebiyi, I. Olaniyan, P. Ezewele & O. Aina. 2014. Occurrence of Newcastle
- Disease and Infectious Bursal Disease Virus Antibodies in Double-Spurred Francolins in Nigeria.
- Journal of Veterinary Medicine. 2014, 1-5. https://doi.org/10.1155/2014/106898.
- Perry, B. D., Kalpravidh, ), P. G. Coleman, H. S. Horst, J. J. Mcdermott, T. F. Randolph & L. J. Gleeson,1999.
- The Economic Impact of Foot and Mouth Disease and Its Control in South-East Asia: a Preliminary
- Assessment With Special Reference to Thailand. Rev. Sci. Tech. Off. Int. Epiz, 18(2): 478–497.
- Sharif, A., T. Ahmad, M. Umer, A. Rehman & Z. Hussain. 2014. Prevention and Control of Newcastle
- Disease. International Journal of Agriculture Innovations and Research, 3(2),454–460.
- Tilahun, M. 2017. Backward Bifurcation in SIRS Malaria Model. 1-22. Http://Arxiv.Org/Abs/1707.00924.
- Yongolo, M. G., A. Machangu & U. Minga. 2002. Newcastle Disease and Infectious Bursal Disease
- Among Free-Range Village Chickens in Tanzania. Characteristics and Parameters of Family Poultry
- Production in Africa, 107–116.
- Yongolo, M. G., H. Christensen, K. Handberg, U. Minga & J. E. Olsen. 2011. on the Origin and
- Diversity of Newcastle Disease Virus in Tanzania. The Onderstepoort Journal of Veterinary Research.
References
Alders, R., P. Spradbrow & M. Young. 2009. Village Chickens, Poverty Alleviation and the
Sustainable Control of Newcastle Disease. Proceedings of An International Conference Held in Dar
Es Salaam, Tanzania, 5–7 October 2005. ACIAR Proceedings No 131, 235.
Alexander, D. J., J. G. Bell & R. G. Alders. 2004. FAO Technology Review: Newcastle Disease With
Special Emphasis on Its Effect on Village Chickens. FAO Animal Production and Health, 4(ISSN
–6019): 55.
Alexander, D. J., R. J. Manvell, J. P. Lowings, K. M. Frost, M. S. Collins, P. H. Russell & J. E. Smith,1997.
Antigenic Diversity and Similarities Detected in Avian Paramyxovirus Type 1 (Newcastle Disease
Virus) Isolates Using Monoclonal Antibodies. Avian Pathology, 26(2): 399–418.
Bhunu, C. P., W. Garira & Z. Mukandavire. 2009. Modeling HIV / AIDS and Tuberculosis Coinfection.
Bulletin of Mathematical Biology, 71, 1745–1780.
Brown, V. R. & S. N. Bevins. 2017. A Review of Virulent Newcastle Disease Viruses in the United
States and the Role of Wild Birds in Viral Persistence and Spread. Veterinary Research, 48(1): 1–
https://doi.org/10.1186/S13567-017-0475-9.
Buonomo, B. & C. Vargas-De-León. 2013. Mathematical Biosciences Stability and Bifurcation
Analysis of a Vector-Bias Model of Malaria Transmission. Mathematical Biosciences, 242(1): 59–
https://doi.org/10.1016/J.Mbs.2012.12.001.
Castillo-Chavez, C. 2004. Dynamical Models of Tuberculosis and Their Applications. Mathematical
Biosciences and Engineering, 1(2): 361–404.
Chingonikaya, E. E. & F. S. Salehe. 2018. Contribution of Local Chicken Production Towards
Improving Peoples Wellbeing : a Case of Peri-Urban Areas of Kinondoni District , Tanzania. Asian
Journal of Advances in Agricultural Research, 5(2): 1–11.
Chuma, F., G. G. Mwanga & V. G. Masanja. 2019. Application of Optimal Control Theory To
Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds As Reservoir of
Disease Virus. Journal of Applied Mathematics. 2019. https://doi.org/10.1155/2019/3024965.
Chuma, F., G. Mwanga & G. Kajunguri. 2018. Modeling the Role of Wild Birds and Environment in
the Dynamics of Newcastle Diseasein Village Chicken. Asian Journal of Mathematics and
Applications. 2018(November): 23.
Daut, E. F., G. Lahodny, M. J. Peterson & R. Ivanek. 2016. Interacting Effects of Newcastle Disease
Transmission and Illegal Trade on a Wild Population of White-Winged Parakeets in Peru: a
Modeling Approach. Plos ONE, 11(1): 1–29. https://doi.org/10.1371/Journal.Pone.0147517.
Dortmans, J. C., G. Koch, P. J. Rottier & B. P. Peeters. 2011. Virulence of Newcastle Disease Virus: What
Is Known So Far? Veterinary Research, 42(1): 1–11. https://doi.org/10.1186/1297-9716-42-122.
Driessche, P. Van Den & J. Watmough. 2002. Reproduction Numbers and Sub-Threshold Endemic
Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180: 29–48.
Edmund, J .R & V. Mwenda. 2018. Poultry Subsector in Tanzania: a Quick Scan. Embassy of the
Kingdom of the Netherlands.
Foppa, I. M. 2015. The Basic Reproductive Number of Tick-Borne Encephalitis Virus: An Empirical
Approach. Journal of Mathematical Biology, January 2006, 13. https://doi.org/10.1007/S00285-005-
-3.
Hartemink, N. A., Randolph, S. E., Davis, S. A. & Heesterbeek, J. A. P. 2008. The Basic Reproduction
Number for Complex Disease Systems : Defining R 0 for Tick-Borne Infections. JSTOR, 171(6):
-754. https://doi.org/10.1086/587530.
Hossain, M., M. Islam, M. Bari, M. Torab & M. Mondal. 2013. Seroprevalence of Newcastle Disease
Virus in Backyard Chickens At Gazipur District of Bangladesh. International Journal of Natural
Sciences, 3(1–4): 22–25.
Hugo, A., O. D. Makinde, S. Kumar & F. F. Chibwana. 2017. Optimal Control and Cost Effectiveness
Analysis for Newcastle Disease Eco-Epidemiological Model in Tanzania. Journal of Biological
Dynamics, 11(1),190–209. https://doi.org/10.1080/17513758.2016.1258093.
Kelatlhegile, G. R. & M. Kgosimore. 2016. Bifurcation Analysis of Vertical Transmission Model With
Preventive Strategy. 0, 492–498. https://doi.org/10.1016/J.Joems.2015.10.001
Lucchetti, J., M. Roy & M. Martcheva. 2009. An Avian Influenza Model and Its Fit To Human Avian
Influenza Cases. Advances in Disease Epidemiology, 1, 1–30.
Mafuta, P., J. Mushanyu, S. Mushayabasa & C. Bhunu. 2013. ’Transmission Dynamics of
Trichomoniasis in Bisexuals’ Without the 'E' Transmission Dynamics of Trichomoniasis in
Bisexuals ’ Without the ‘ E .’ World Journal of Modelling and Simulation, 9(4), 302–320.
Mcdermott, J., P. Coleman & T. Randolph. 2000. Methods for Assessing the Impact of Infectious Diseases
of Livestock - Their Role in Improving the Control of Newcastle Disease in Southern Africa. Aciar.
Mengesha, M. 2012. Indigeneous Chicken Production and the Innate Characteristics. Asian Journal
of Poultry Science, 6(2): 56–64.
Michael, S., J. Stapleton & B. I. Shapiro. 2017. Tanzania Livestock Master Plan: Key Findings. ILRI
Internal Report, Brief 1 Oc(Nairobi, Kenya), 1-4.
Mlozi, M. R. S., A.V.M. Kakengi, U. M. Minga, A. M. Mtambo & J. E. Olsen. 2003. Marketing of Free
Range Local Chickens in Morogoro and Kilosa Urban Markets, Tanzania. Livestock Research for
Rural Development, 15(14).
Munir, M. T. & M. R. Chowdhury. 2016. Emergence of New Sub-Genotypes of Newcastle Disease
Virus in Pakistan. J Avian Res, 2(1): 1–7.
Nyerere, N. & L. S. Luboobi. 2014. Bifurcation and Stability Analysis of the Dynamics of Tuberculosis
Model Incorporating, Vaccination, Screening and Treatment. Commun. Math. Biol. Neurosci.
Oluwayelu, D. O., A. I. Adebiyi, I. Olaniyan, P. Ezewele & O. Aina. 2014. Occurrence of Newcastle
Disease and Infectious Bursal Disease Virus Antibodies in Double-Spurred Francolins in Nigeria.
Journal of Veterinary Medicine. 2014, 1-5. https://doi.org/10.1155/2014/106898.
Perry, B. D., Kalpravidh, ), P. G. Coleman, H. S. Horst, J. J. Mcdermott, T. F. Randolph & L. J. Gleeson,1999.
The Economic Impact of Foot and Mouth Disease and Its Control in South-East Asia: a Preliminary
Assessment With Special Reference to Thailand. Rev. Sci. Tech. Off. Int. Epiz, 18(2): 478–497.
Sharif, A., T. Ahmad, M. Umer, A. Rehman & Z. Hussain. 2014. Prevention and Control of Newcastle
Disease. International Journal of Agriculture Innovations and Research, 3(2),454–460.
Tilahun, M. 2017. Backward Bifurcation in SIRS Malaria Model. 1-22. Http://Arxiv.Org/Abs/1707.00924.
Yongolo, M. G., A. Machangu & U. Minga. 2002. Newcastle Disease and Infectious Bursal Disease
Among Free-Range Village Chickens in Tanzania. Characteristics and Parameters of Family Poultry
Production in Africa, 107–116.
Yongolo, M. G., H. Christensen, K. Handberg, U. Minga & J. E. Olsen. 2011. on the Origin and
Diversity of Newcastle Disease Virus in Tanzania. The Onderstepoort Journal of Veterinary Research.