Modeling and analysis of the transmission of avian spirochetosis with non-singular and non-local kernel

References

• Ataliba AC, Resende JS, Yoshinari N, Labruna MB. 2007. Isolation and molecular characterization of a Brazilian strain of Borrelia anserina, the agent of fowl spirochaetosis. Res Vet Sci. 83(2):145–149.
   PubMed Web of Science ®Google Scholar
• Atangana A, Baleanu D. 2016. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Thermal Science. 20(2):763–769.
   Google Scholar
• Bada OI, Oke AS, Mutuku WN, Aye PO. 2020. Analysis of the dynamics of SI-SI-SEIR Avian influenza A (H7N9) epidemic model with re-infection. EJMS. 5(1):43–73.
   Google Scholar
• Barbour AG, Hayes SF. 1986. Biology of Borrelia species. Microbiol Rev. 50(4):381–400.
   PubMedGoogle Scholar
• Boulaaras S, Rehman ZU, Abdullah FA, Jan R, Abdalla M, Jan A. 2023. Coronavirus dynamics, infections and preventive interventions using fractional-calculus analysis. MATH. 8(4):8680–8701.
   Google Scholar
• Daut EF, Lahodny G, Jr, Peterson MJ, Ivanek R. 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):e0147517.
   PubMed Web of Science ®Google Scholar
• Diekmann O, Heesterbeek JAP. 2000. Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Vol. 5. John Wiley & Sons.
   Google Scholar
• Fox W. 2010. Tick-borne diseaserisks and reality. Borreliosis & Associated Diseases Awareness UK, Rotherham.
   Google Scholar
• Hee-Dae KWON. 2008. Applications of optimal control theory to mathematical models of biological systems, 1. Proceedings of the Korean Society of Industrial Applied Mathematics Conference. 4(3):27–30.
   Google Scholar
• Jan A, Jan R, Khan H, Zobaer MS, Shah R. 2020. Fractional-order dynamics of Rift Valley fever in ruminant host with vaccination. Commun Math Biol Neurosci. 2020:1–32.
   Google Scholar
• Jan R, Boulaaras S, Ahmad H, Jawad M, Zubair S, Abdalla M. 2023. A robust study of tumor-immune cells dynamics through non-integer derivative. Fractal Fract. 7(2):164.
   Web of Science ®Google Scholar
• Jan R, Khan MA, Kumam P, Thounthong P. 2019. Modeling the transmission of dengue infection through fractional derivatives. Chaos Solitons Fractals. 127:189–216.
   Web of Science ®Google Scholar
• Jan R, Qureshi S, Boulaaras S, Pham VT, Hincal E, Guefaifia R. 2023. Optimization of the fractional-order parameter with the error analysis for human immunodeficiency virus under Caputo operator. DCDS-S. 2023. doi:10.3934/dcdss.2023010.
   Google Scholar
• Kaikabo AA, Mustapha A, Yaroro II. 2007. Avian spirochaetosis associated with colisepticemia in free ranging white breasted guinea fowls (Numida meleagris pallas) in arid region of Nigeria: a case report. Anim Prod Res Adv. 2(3):161–163.
   Google Scholar
• Kriesel A, Meyer M, Peterson G. 2009. Mathematical modeling of tick-borne encephalitis in humans. J Undergrad Res Minnesota State Univ Mankato. 9(1):9.
   Google Scholar
• Lisbôa RS, Teixeira RC, Rangel CP, Santos HA, Massard CL, Fonseca AH., 2009. Avian spirochetosis in chickens following experimental transmission of Borrelia anserina by Argas (Persicargas) miniatus. Avian Dis. 53(2):166–168.
   PubMed Web of Science ®Google Scholar
• Oke AS. 2017. Convergence of differential transform method for ordinary differential equations. JAMCS. 24(6):1–17.
   Google Scholar
• Oke AS, Bada OI, Rasaq G, Adodo V. 2022. Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection. Math Methods Appl Sci. 45(1):137–149.
   PubMed Web of Science ®Google Scholar
• Porter R. 2011. Mathematical models of a tick borne disease in a British game bird with potential management strategies.
   Google Scholar
• Ramadan HS, Padmanaban S, Mosaad MI. 2022. Metaheuristic-based near-optimal fractional order PI controller for on-grid fuel cell dynamic performance enhancement. Electr Power Syst Res. 208:107897.
   Web of Science ®Google Scholar
• Ros R, Pugliese A, Norman R, Hudson PJ. 2003. Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation. J Theor Biol. 224(3):359–376.
   PubMed Web of Science ®Google Scholar
• Shah Z, Jan R, Kumam P, Deebani W, Shutaywi M. 2021. Fractional dynamics of HIV with source term for the supply of new CD4+ T-cells depending on the viral load via caputofabrizio derivative. Molecules. 26(6):1806.
   PubMed Web of Science ®Google Scholar
• Switkes J, Nannyonga B, Mugisha JYT, Nakakawa J. 2016. A mathematical model for Crimean-Congo haemorrhagic fever: tick-borne dynamics with conferred host immunity. J Biol Dyn. 10(1):59–70.
   PubMed Web of Science ®Google Scholar
• Tang TQ, Shah Z, Jan R, Alzahrani E. 2022. Modeling the dynamics of tumorimmune cells interactions via fractional calculus. Eur Phys J Plus. 137(3):1–18.
   PubMed Web of Science ®Google Scholar
• Tang TQ, Shah Z, Jan R, Deebani W, Shutaywi M. 2021. A robust study to conceptualize the interactions of CD4+ T-cells and human immunodeficiency virus via fractional-calculus. Phys Scr. 96(12):125231.
   Web of Science ®Google Scholar
• Toufik M, Atangana A. 2017. New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models. Eur Phys J Plus. 132(10):1–16.
   Web of Science ®Google Scholar
• Uwakwe JI, Inyama SC, Emerenini BO. 2017. Mathematical model and optimal control of the transmission dynamics of avian spirochaetosis. Journal of Applied Mathematics and Physics. 8(2):270–293.
   Google Scholar
• Van den Driessche P, Watmough J. 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 180(1–2):29–48.
   PubMed Web of Science ®Google Scholar
• Zafar ZUA, Hussain MT, Inc M, Baleanu D, Almohsen B, Oke AS, Javeed S. 2022. Fractional-order dynamics of human papillomavirus. Results Phys. 34:105281.
   Web of Science ®Google Scholar