Finite difference method for transmission dynamics of Contagious Bovine Pleuropneumonia

Sait Kıkpınar; Mahmut Modanli; Ali Akgül; Fahd Jarad; Sait Kıkpınar; Mahmut Modanli; Ali Akgül; Fahd Jarad

doi:10.3934/math.2022574

AIMS Mathematics

2022, Volume 7, Issue 6: 10303-10314. doi: 10.3934/math.2022574

Previous Article Next Article

Research article

Finite difference method for transmission dynamics of Contagious Bovine Pleuropneumonia

1.
Harran University, Faculty of Veterinary Medicine, 63300, Sanliurfa/Turkey, ORCID NO: 0000-0001-9065-1904
2.
Harran University, Faculty of Sciences and Arts, Department of Mathematics, 63300, Sanliurfa/Turkey, ORCID NO: 0000-0002-7743-3512
3.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
4.
Department of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey
5.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 30 December 2021 Revised: 28 February 2022 Accepted: 10 March 2022 Published: 24 March 2022
MSC : 34A08; 65N06

In this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.
- Contagious Bovine Pleuropneumonia,
- Caputo differential equation,
- finite difference method
Citation: Sait Kıkpınar, Mahmut Modanli, Ali Akgül, Fahd Jarad. Finite difference method for transmission dynamics of Contagious Bovine Pleuropneumonia[J]. AIMS Mathematics, 2022, 7(6): 10303-10314. doi: 10.3934/math.2022574

Related Papers:

Abstract

In this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.

References

[1]	A. A. Aligaz, J. M. W. Munganga, Analysis of a mathematical model of the dynamics of contagious bovine pleuropneumonia, Texts Biomath., 1 (2017), 64–80. https://doi.org/10.11145/texts.2017.12.253 doi: 10.11145/texts.2017.12.253
[2]	A. A. Aligaz, J. M. W. Munganga, Mathematical modelling of the transmission dynamics of contagious bovine pleuropneumonia with vaccination and antibiotic treatment, J. Appl. Math., 2019. https://doi.org/10.1155/2019/2490313 doi: 10.1155/2019/2490313
[3]	A. Ssematimba, J. Jores, J. C. Mariner, Mathematical modelling of the transmission dynamics of contagious bovine pleuropneumonia reveals minimal target profiles for improved vaccines and diagnostic assays, PLoS One, 10 (2015), e0116730. https://doi.org/10.1371/journal.pone.0116730 doi: 10.1371/journal.pone.0116730
[4]	N. B. Alhaji, P. I. Ankeli, L. T. Ikpa, O. O. Babalobi, Contagious Bovine Pleuropneumonia: Challenges and prospects regarding diagnosis and control strategies in Africa, Vet. Med.: Res. Rep., 11 (2020), 71. https://doi.org/10.2147/VMRR.S180025 doi: 10.2147/VMRR.S180025
[5]	E. M. Vilei, J. Frey, Detection of Mycoplasma mycoides subsp. mycoides SC in bronchoalveolar lavage fluids of cows based on a TaqMan real-time PCR discriminating wild type strains from an lppQ-mutant vaccine strain used for DIVA-strategies, J. Microbiol. Meth., 81 (2010), 211–218. https://doi.org/10.1016/j.mimet.2010.03.025 doi: 10.1016/j.mimet.2010.03.025
[6]	I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, 1998.
[7]	J. C. Mariner, J. McDermott, J. A. P. Heesterbeek, G. Thomson, P. L. Roeder, S. W. Martin, A heterogeneous population model for contagious bovine pleuropneumonia transmission and control in pastoral communities of East Africa, Prev. Vet. Med., 73 (2006), 75–91. https://doi.org/10.1016/j.prevetmed.2005.09.002 doi: 10.1016/j.prevetmed.2005.09.002
[8]	J. Jores, J. C. Mariner, J. Naessens, Development of an improved vaccine for contagious bovine pleuropneumonia: An African perspective on challenges and proposed actions, Vet. Res., 44 (2013), 1–5. https://doi.org/10.1186/1297-9716-44-122 doi: 10.1186/1297-9716-44-122
[9]	J. O. Onono, B. Wieland, J. Rushton, Estimation of impact of contagious bovine pleuropneumonia on pastoralists in Kenya, Pre. Vet. Med., 115 (2014), 122–129. https://doi.org/10.1016/j.prevetmed.2014.03.022 doi: 10.1016/j.prevetmed.2014.03.022
[10]	M. J. Otte, R. Nugent, A. McLeod, Transboundary animal diseases: Assessment of socio-economic impacts and institutional responses, Rome, Italy: Food Agriculture Organization, (2004), 119–126.
[11]	N. Abdela, N. Yune, Seroprevalence and distribution of contagious bovine pleuropneumonia in Ethiopia: update and critical analysis of 20 years (1996–2016) reports, Front. Vet. Sci., 4 (2017), 100. https://doi.org/10.3389/fvets.2017.00100 doi: 10.3389/fvets.2017.00100
[12]	N. E. Tambi, W. O. Maina, C. Ndi, An estimation of the economic impact of contagious bovine pleuropneumonia in Africa, Rev. Sci. Tech. OIE., 25 (2006), 999–1011. https://doi.org/10.20506/rst.25.3.1710 doi: 10.20506/rst.25.3.1710
[13]	T. S. Gorton, M. M. Barnett, T. Gull, R. A. French, Z. Lu, G. F. Kutish, et al., Development of real-time diagnostic assays specific for Mycoplasma mycoides subspecies mycoides Small Colony, Vet. Microbiol., 111 (2005), 51–58. https://doi.org/10.1016/j.vetmic.2005.09.013 doi: 10.1016/j.vetmic.2005.09.013
[14]	E. Sousa, How to approximate the fractional derivative of order 1 < α≤ 2, Int. J. Bifurcat. Chaos, 22 (2012), 1250075. https://doi.org/10.1142/S0218127412500757 doi: 10.1142/S0218127412500757
[15]	Q. M. Al-Mdallal, M. A. Hajji, T. Abdeljawad, On the iterative methods for solving fractional initial value problems: New perspective, J. Fractional Calculus Nonlinear Syst, 2 (2021), 76–81. https://doi.org/10.48185/jfcns.v2i1.297 doi: 10.48185/jfcns.v2i1.297
[16]	A. Khan, H. M. Alshehri, T. Abdeljawad, Q. M. Al-Mdallal, H. Khan, Stability analysis of fractional nabla difference COVID-19 model, Results Phys., 22 (2021), 103888. https://doi.org/10.1016/j.rinp.2021.103888 doi: 10.1016/j.rinp.2021.103888
[17]	M. Lesnoff, G. Laval, P. Bonnet, K. Chalvet-Monfray, R. Lancelot, F. Thiaucourt, A mathematical model of the effects of chronic carriers on the within-herd spread of contagious bovine pleuropneumonia in an African mixed crop–livestock system, Pre. Vet. Med., 62 (2004), 101–117. https://doi.org/10.1016/j.prevetmed.2003.11.009 doi: 10.1016/j.prevetmed.2003.11.009
[18]	A. A. Aligaz, J. M. Munganga, Modelling the transmission dynamics of Contagious Bovine Pleuropneumonia in the presence of antibiotic treatment with limited medical supply, Math. Model. Anal., 26 (2021), 1–20. https://doi.org/10.3846/mma.2021.11795 doi: 10.3846/mma.2021.11795

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)