In this paper, nonlinear fractional order Ebola virus mathematical model is discussed for the complex transmission of the epidemic problems. We developed the fractional order Ebola virus transmission model for the treatment and control to reduce its effect on a population which play an important role for public health. Qualitative analysis has been made to verify the the steady state and uniqueness of the system is also developed for reliable results. Caputo fractional derivative operator ϕ_{i} ∈ (0,1] works to achieve the fractional differential equations. Laplace with Adomian Decomposition Methodsuccessfully solved the fractional differential equations. Ultimately, numerical simulations are also developed to evaluate the effects of the device parameter on spread of disease and effect of fractional parameter ϕ_{i} on obtained solution which can also be assessed by tabulated results.
Citation: Ali Raza, Muhammad Farman, Ali Akgül, Muhammad Sajid Iqbal, Aqeel Ahmad. Simulation and numerical solution of fractional order Ebola virus model with novel technique[J]. AIMS Bioengineering, 2020, 7(4): 194-207. doi: 10.3934/bioeng.2020017
In this paper, nonlinear fractional order Ebola virus mathematical model is discussed for the complex transmission of the epidemic problems. We developed the fractional order Ebola virus transmission model for the treatment and control to reduce its effect on a population which play an important role for public health. Qualitative analysis has been made to verify the the steady state and uniqueness of the system is also developed for reliable results. Caputo fractional derivative operator ϕ_{i} ∈ (0,1] works to achieve the fractional differential equations. Laplace with Adomian Decomposition Methodsuccessfully solved the fractional differential equations. Ultimately, numerical simulations are also developed to evaluate the effects of the device parameter on spread of disease and effect of fractional parameter ϕ_{i} on obtained solution which can also be assessed by tabulated results.
[1] | Agusto FB, Teboh-Ewungkem MI, Gumel AB (2015) Mathematical assessment of the effect of traditional beliefs and customs on the transmission dynamics of the 2014 Ebola outbreaks. BMC Med 13: 96. doi: 10.1186/s12916-015-0318-3 |
[2] | Amundsen SB (1998) Historical analysis of the Ebola virus: prospective implications for primary care nursing today. Clin Excell Nurse Pract 2: 343-351. |
[3] | Baseler L, Chertow DS, Johnson KM, et al. (2017) The pathogenesis of Ebola virus disease. Annu Rev Pathol Mech Dis 12: 387-418. doi: 10.1146/annurev-pathol-052016-100506 |
[4] | Berge T, Lubuma JMS, Moremedi GM, et al. (2017) A simple mathematical model for Ebola in Africa. J Biol Dynam 11: 42-74. doi: 10.1080/17513758.2016.1229817 |
[5] | Agusto FB (2017) Mathematical model of Ebola transmission dynamics with relapse and reinfection. Math Biosci 283: 48-59. doi: 10.1016/j.mbs.2016.11.002 |
[6] | Mate SE, Kugelman JR, Nyenswah TG, et al. (2015) Molecular evidence of sexual transmission of Ebola virus. New Engl J Med 373: 2448-2454. doi: 10.1056/NEJMoa1509773 |
[7] | Althaus CL (2014) Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa. doi: 10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288 |
[8] | Weitz JS, Dushoff J (2015) Modeling post-death transmission of Ebola: challenges for inference and opportunities for control. Sci Rep 5: 8751. doi: 10.1038/srep08751 |
[9] | Thompson RN, Hart WS (2018) Effect of confusing symptoms and infectiousness on forecasting and control of Ebola outbreaks. Clin Infect Dis 67: 1472-1474. doi: 10.1093/cid/ciy248 |
[10] | Hart WS, Hochfilzer LFR, Cunniffe NJ, et al. (2019) Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection. Epidemics 29: 100371. doi: 10.1016/j.epidem.2019.100371 |
[11] | Singh J, Kumar D, Hammouch Z, et al. (2018) A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Appl Math Comput 316: 504-515. |
[12] | Kumar D, Singh J, Baleanu D (2018) Analysis of regularized long-wave equation associated with a new fractional operator with Mittag–Leffler type kernel. Phys A 492: 155-167. doi: 10.1016/j.physa.2017.10.002 |
[13] | Farman M, Saleem MU, Ahmad A, et al. (2018) Analysis and numerical solution of SEIR epidemic model of measles with non-integer time fractional derivatives by using Laplace Adomian Decomposition Method. Ain Shams Eng J 9: 3391-3397. doi: 10.1016/j.asej.2017.11.010 |
[14] | Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 1: 73-85. |
[15] | Losada J, Nieto JJ (2015) Properties of a new fractional derivative without singular kernel. Prog Fract Differ Appl 1: 87-92. |
[16] | Atangana A, Baleanu D (2016) New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci 20: 763-769. doi: 10.2298/TSCI160111018A |
[17] | Saleem MU, Farman M, Ahmad A, et al. (2019) Stability analysis and control of fractional order diabetes mellitus model for artificial pancreas. Punjab Univ J Math 51: 85-101. |
[18] | Jarad F, Abdeljawad T, Hammouch Z (2018) On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative. Chaos Soliton Fract 117: 16-20. doi: 10.1016/j.chaos.2018.10.006 |
[19] | Baleanu D, Jajarmi A, Hajipour M (2018) On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dynam 94: 397-414. doi: 10.1007/s11071-018-4367-y |
[20] | Ndanguza D, Tchuenche JM, Haario H (2013) Statistical data analysis of the 1995 Ebola outbreak in the Democratic Republic of Congo. Afr Mat 24: 55-68. doi: 10.1007/s13370-011-0039-5 |
[21] | Rachah A, Torres DFM (2015) Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa. Discrete Dyn Nat Soc 2015: 842792. doi: 10.1155/2015/842792 |
[22] | Jiang S, Wang K, Li C, et al. (2017) Mathematical models for devising the optimal Ebola virus disease eradication. J Transl Med 15: 124. doi: 10.1186/s12967-017-1224-6 |
[23] | Chretien JP, Riley S, George DB (2015) Mathematical modeling of the West Africa Ebola epidemic . doi: 10.7554/eLife.09186 |
[24] | Muhammad Altaf K, Atangana A (2019) Dynamics of Ebola disease in the framework of different fractional derivatives. Entropy 21: 303. doi: 10.3390/e21030303 |