×
Ahmed, Nauman; Shaikh, Tahira Sumbal; Rafiq, Muhammad; Eldin, Sayed M.; Ganie, Abdul Hamid; Ali, Mubasher; Raza, Ali; Khan, Ilyas; Khan, M. I.

Structure preserving splitting techniques for Ebola reaction-diffusion epidemic system. (English) Zbl 1519.92233

Fractals 31, No. 2, Article ID 2340041, 12 p. (2023).

MSC:

92D30 Epidemiology
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations

Keywords:

Ebola infection; reaction-diffusion system; splitting techniques; nonstandard finite differences; simulations
Cite Review PDF
Full Text: DOI

References:

[1] WHO: Ebola response roadmap situation report, World Health Organization (2015), http://www.who.int/csr/disease/ebola/situation-reports/en/ (accessed on 5 February 2015).
[2] Schiefelin, J. S. and Jacob, S. T., Raising the standard for clinical care of patients with Ebola virus disease, Lancet Infect. Dis.15 (2015) 1247-1248.
[3] Towers, S., Patterson-Lomba, O. and Castillo-Chavez, C., Temporal variations in the effective reproduction number of the 2014 west Africa ebola outbreak, PLoS Curr. (2014), https://doi.org/10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908.
[4] Webb, G., Browne, C., Huo, X., Seydi, O., Seydi, M. and Magal, P., A model of the 2014 ebola epidemic in west Africa with contact tracing, PLoS Curr. (2015), https://doi.org/10.1371/currents.outbreaks.846b2a31ef37018b7d1126a9c8adf22a.
[5] Yamin, D., Gertler, S., Ndefo-Mbah, M. L. and Galvani, A. P., Effect of Ebola progression on transmission and control in Liberia, Ann. Int. Med.162 (2015) 11-17.
[6] Pandey, A.et al., Strategies for containing Ebola in West Africa, Science346 (2014) 991-995, https://doi.org/10.1126/science.1260612.
[7] Rivers, C. M., Lofgren, E. T., Marathe, M., Eubank, S. and Lewis, B. L., Modeling the impact of interventions on an epidemic of ebola in sierra leone and liberia, PLoS Curr. (2014), https://doi.org/10.1371/currents.outbreaks.fd38dd85078565450b0be3fcd78f5ccf.
[8] Hsieh, Y. H., Temporal course of 2014 Ebola virus disease (EVD) outbreak in West Africa elucidated through morbidity and mortality data: A tale of three Countries, PLoS One10 (2015), https://doi.org/10.1371/journal.pone.0140810.
[9] Jiang, S.et al., Mathematical models for devising the optimal Ebola virus disease eradication, J. Transl. Med.15 (2017) 124, https://doi.org/10.1186/s12967-017-1224-6.
[10] Tulu, T. W., Tian, B. and Wu, Z., Mathematical modeling, analysis and Markov chain Monte Carlo simulation of ebola epidemics, Results Phys.7 (2017) 962-968.
[11] Dong, F., Xu, D., Wang, Z. and Dong, M., Evaluation of ebola spreading in west africa and decision of optimal medicine delivery strategies based on mathematical models, Infect. Genet. Evol.36 (2015) 35-40.
[12] Althaus, C. L., Estimating the reproduction number of ebola virus (EBOV) during the 2014 outbreak in West Africa, PLoS Curr.6 (2014), https://doi.org/10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288.
[13] Chowell, G. and Nishiura, H., Transmission dynamics and control of ebola virus disease (EVD): A review, BMC Med.12 (2014) 196.
[14] Ngwa, G. A. and Teboh-Ewungkem, M. I., A mathematical model with quarantine states for the dynamics of ebola virus disease in human populations, Comput. Math. Methods Med.2016 (2016) 9352725. · Zbl 1359.92108
[15] Weitz, J. S. and Dushoff, J., Modeling post-death transmission of ebola: Challenges for inference and opportunities for control, Sci. Rep.5 (2015) 8751.
[16] Ndanguza, D., Mbalawata, I. S., Haario, H. and Tchuenche, J. M., Analysis of bias in an ebola epidemic model by extended Kalman filter approach, Math. Comput. Simul.142 (2017) 113-129. · Zbl 1540.92217
[17] Diaz, P., Constantine, P., Kalmbach, K., Jones, E. and Pankavich, S., A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation, Appl. Math. Comput.324 (2018) 141-155. · Zbl 1426.92072
[18] Atangana, A. and Goufo, E. F. D., On the mathematical analysis of ebola hemorrhagic fever: Deathly infection disease in West African countries, BioMed. Res. Int.2014 (2014) 261383.
[19] Jiang, S.et al., Mathematical models for devising the optimal ebola virus disease eradication, J. Transl. Med.15 (2017) 124.
[20] Berge, T., Lubuma, J. M. S., Moremedi, G. M., Morris, N. and Kondera-Shava, R., A simple mathematical model for ebola in africa, J. Biol. Dyn.11 (2017) 42-74. · Zbl 1448.92276
[21] Xia, Z. Q.et al., Modeling the transmission dynamics of ebola virus disease in Liberia, Sci. Rep.5 (2015) 13857.
[22] Khan, A., Naveed, M., Dur-e-Ahmad, M. and Imran, M., Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone, Infect. Dis. Poverty4 (2015) 13.
[23] Chowell, G., Hengartner, N. W., Castillo-Chavez, C., Fenimore, P. W. and Hyman, J. M., The basic reproductive number of Ebola and the effects of public health measures: The cases of Congo and Uganda, J. Theor. Biol.229 (2004) 119-126. · Zbl 1440.92062
[24] Goufo, E. F. D., Pene, M. K. and Mugisha, S., Stability analysis of epidemic models of ebola hemorrhagic fever with nonlinear transmission, J. Nonlinear Sci. Appl.9 (2016) 4191-4205. · Zbl 1345.92139
[25] Agusto, F. B., Teboh-Ewungkem, M. I. and Gumel, A. B., Mathematical assessment of the effect of traditional beliefs and customs on the transmission dynamics of the 2014 ebola outbreaks, BMC Med.13 (2015) 96.
[26] Luo, D.et al., Effect of sexual transmission on the west africa ebola outbreak in 2014: A mathematical modelling study, Sci. Rep.9 (2019) 1653.
[27] Denes, A. and Gumel, A. B., Modeling the impact of quarantine during an outbreak of ebola virus disease, Infect. Dis. Model.4 (2019) 12-27.
[28] Sharomi, O. and Malik, T., Optimal control in epidemiology, Ann. Oper. Res.251 (2017) 55-71. · Zbl 1373.92140
[29] Zakary, O., Rachik, M. and Elmouki, I., A multi-regional epidemic model for controlling the spread of ebola: Awareness, treatment, and travel-blocking optimal control approaches, Math. Methods Appl. Sci.40 (2017) 1265-1279. · Zbl 1360.92123
[30] Bonyah, E., Badu, K. and Asiedu-Addo, S. K., Optimal control application to an ebola model, Asian Pacific J. Tropical Biomed.6 (2016) 283-289.
[31] Ahmad, M. D., Usman, M., Khan, A. and Imran, M., Optimal control analysis of ebola disease with control strategies of quarantine and vaccination, Infect. Dis. Poverty5 (2016) 72.
[32] Gatto, M., Bertuzzo, E., Mari, L., Miccoli, S., Carraro, L., Casagrandi, R. and Rinaldo, A., Spread and dynamics of the covid-19 epidemic in italy: Effects of emergency containment measures, Proc. Natl. Acad. Sci. U. S. A.117(19) (2020) 10484-10491.
[33] Guan, Y.et al., Isolation and characterization of viruses related to the SARS coronavirus from animals in southern China, Science302 (2003) 276-278.
[34] Ruan, S. and Wang, W., Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differ. Equ.188 (2003) 135-163. · Zbl 1028.34046
[35] Partohaghighi, M., Akgl, A. and Alqahtani, R. T., New type modelling of the circumscribed self-excited spherical attractor, Mathematics10 (2022) 732, https://doi.org/10.3390/math10050732.
[36] Chen, W., Sun, H. and Li, X., Typical applications of fractional differential equations, in Fractional Derivative Modeling in Mechanics and Engineering (Springer, 2022), pp. 159-284, https://doi.org/10.1007/978-981-16-8802-7-5.
[37] Ravichandran, C., Jothimani, K., Nisar, K. Sooppy, Mahmoud, E. E. and Yahia, I. S., An interpretation on controllability of Hilfer fractional derivative with nondense domain, Alex. Eng. J.61(12) (2022) 9941-9948.
[38] Goufo, E. F. Doungmo, Ravichandran, C. and Birajdar, G. A., Self-similarity techniques for chaotic attractors with many scrolls using step series switching, Math. Model. Anal.26(4) (2021) 591-611. · Zbl 1497.28004
[39] Ravichandran, C., Munusamy, K., Nisar, K. S. and Valliammal, N., Results on neutral partial integrodifferential equations using Monch-Krasnosel’skii fixed point theorem with nonlocal conditions, Fractal Fract.6(2) (2022) 75.
[40] Nisar, K. S., Logeswari, K., Vijayaraj, V., Baskonus, H. M. and Ravichandran, C., Fractional order modeling the Gemini virus in Capsicum annuum with optimal control, Fractal Fract.6(2) (2022) 61.
[41] Yong-Ki, M., Kamalendra, K., Rohit, P., Anurag, S., Nisar, K. S. and Vijayakumar, V., An investigation on boundary controllability for Sobolev-type neutral evolution equations of fractional order in Banach space, AIMS Math.7(7) (2022) 11687-11707.
[42] Julien, A., Richard, J. and van den Driessche, P., Quarantine in a multi-species epidemic model with spatial dynamics, Math. Biosci.206 (2007) 46-60. · Zbl 1124.92042
[43] Xia, Y., Bjrnstad, O. N. and Grenfell, B. T., Measles metapopulation dynamics: A gravity model for epidemiological coupling and dynamics, Am. Nat.164(2) (2004) 267-281, https://doi.org/10.1086/422341.
[44] Yong-Ki, M., Kamalendra, K., Rakesh, K., Rohit, P., Shukla, A. and Vijayakumar, V., Discussion on boundary controllability of nonlocal fractional neutral integrodifferential evolution systems, AIMS Math.7(5) (2022) 7642-7656.
[45] Vijayakumar, V. and Udhayakumar, R., Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay, Chaos Solitons Fractals139 (2020) 110019. · Zbl 1490.93018
[46] Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Nisar, K. Sooppy and Shukla, A., A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order \(1<r<2\), Math. Comput. Simul.190 (2021) 1003-1026. · Zbl 1540.93009
[47] Yong-Ki, M., Kumar, K., Patel, R., Shukla, A., Nisar, K. S. and Vijayakumar, V., An investigation on boundary controllability for Sobolev-type neutral evolution equations of fractional order in Banach space, AIMS Math.7(7) (2022) 11687-11707.
[48] Raja, M. M., Vijayakumar, V., Shukla, A., Nisar, K. P., Sakthivel, N. and Kaliraj, K., Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order, Opt. Control Appl. Methods43(4) (2022) 996-1019. · Zbl 1531.93030
[49] Vijayakumar, V., Ravichandran, C., Nisar, K. S. and Kucche, K. D., New discussion on approximate controllability results for fractional Sobolev type Volterra-Fredholm integro-differential systems of order \(1<r<2\), Numer. Methods Partial Differ. Equ. (2021) 1-19, https://doi.org/10.1002/num.22772. · Zbl 07840123
[50] Area, I., Ndayrou, F., NdaIrou, F., Nieto, J. J. and Silva, C. J., Ebola model and optimal control with vaccination constraints, J. Ind. Manag. Optim.14 (2018) 427-446. · Zbl 1412.49005
[51] Grigorieva, E. V., Deignan, P. B. and Khailov, E. N., Optimal control problem for a seir type model of ebola epidemics, Rev. Mat.: Teor. Apl.24 (2017) 79-96. · Zbl 1373.92121
[52] R. C. Harwood, Operator splitting method and applications for semilinear parabolic partial differential equations, Ph.D. Dissertation, Pullman Dept. Math., Washington State University (2011).
[53] Harwood, R. C., Manoranjan, V. S. and Edwards, D. B., Lead-acid battery model under discharge with a fast splitting method, IEEE Trans. Energy Convers.26 (2011) 1109-1117.
[54] Yanenko, N. N., The Method of Fractional Steps, (Springer-Verlag, 1971). · Zbl 0209.47103
[55] Zharnitsky, V., Averaging for split-step scheme, Nonlinearity16 (2003) 1359-1366. · Zbl 1042.65077
[56] Chakrabrty, A., Singh, M., Lucy, B. and Ridland, P., Predator-prey model with pry-taxis and diffusion, Math. Comput. Model.46 (2007) 482-498, https://doi.org/10.1016/j.mcm.2006.10.010. · Zbl 1132.35395
[57] Mickens, R. E., Nonstandard Finite Difference Models of Differential Equations (World Scientific, 1994). · Zbl 0810.65083
[58] Ahmed, N., Rafiq, M., Baleanu, D. and Rehman, M. A., Spatio-temporal numerical modeling of auto-catalytic brusselator model, Rom. J. Phys.64 (2019) 1-14.
[59] Ahmed, N., Rafiq, M., Rehman, M. A., Iqbal, M. S. and Ali, M., Numerical modeling of three dimensional Brusselator reaction diffusion system, AIP Adv.9 (2019) 15205.
[60] Ahmed, N., Tahira, S. S., Imran, M., Rafiq, M., Rehman, M. A. and Younis, M., Numerical analysis of auto-catalytic glycolysis model, AIP Adv.9 (2019) 85213.
[61] Ahmed, N., Wei, Z., Baleanu, D., Rafiq, M. and Rehman, M. A., Spatio-temporal numerical modeling of reaction-diffusion measles epidemic system, Chaos29 (2019) 103101. · Zbl 1425.92172
[62] Macias-Diaz, J. E., A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives, J. Comput. Phys.351 (2017) 40-58, https://doi.org/10.1016/j.jcp.2017.09.028. · Zbl 1380.65164
[63] Macias-Diaz, J. E. and Puri, A., An explicit positivity-preserving finite-difference scheme for the classical Fisher-Kolmogorov-Petrovsky-Piscounov equation, Appl. Math. Comput.218 (2012) 5829-5837. · Zbl 1244.65125
[64] Macias-Diaz, J. E., Ahmed, N. and Rafiq, M., Analysis and nonstandard numerical design of a discrete three-dimensional hepatitis B epidemic model, Mathematics7 (2019) 1157.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.