JavaScript is disabled for your browser. Some features of this site may not work without it.
| dc.contributor.author | El-Sayed A.M.A. | |
| dc.contributor.author | Arafa A.A.M. | |
| dc.contributor.author | Khalil M. | |
| dc.contributor.author | Sayed A. | |
| dc.contributor.other | Department of mathematics | |
| dc.contributor.other | Faculty of Science | |
| dc.contributor.other | Alexandria University | |
| dc.contributor.other | Alexandria | |
| dc.contributor.other | Egypt; Department of Mathematics | |
| dc.contributor.other | Faculty of Science | |
| dc.contributor.other | Port Said University | |
| dc.contributor.other | Port Said | |
| dc.contributor.other | Egypt; Department of Mathematics | |
| dc.contributor.other | Faculty of Engineering | |
| dc.contributor.other | October University for Modern Sciences and Arts (MSA University) | |
| dc.contributor.other | Giza | |
| dc.contributor.other | Egypt | |
| dc.date.accessioned | 2020-01-09T20:41:17Z | |
| dc.date.available | 2020-01-09T20:41:17Z | |
| dc.date.issued | 2017 | |
| dc.identifier.issn | 23569336 | |
| dc.identifier.other | https://doi.org/10.18576/pfda/030404 | |
| dc.identifier.uri | http://www.naturalspublishing.com/files/published/12g3g36uc8nxq1.pdf | |
| dc.description | Scopus | |
| dc.description.abstract | An epidemiological fractional order model which displays backward bifurcation for some parameters values, is studied in this paper. Because integer order of such model does not convey any information about the effect of the memory or learning mechanism of human population which influences disease transmission, we use the fractional order model in which the memory effect is considered well. As the fractional derivative is considered as the memory index, so the goal of this paper is to study the impact of fractional order derivative on the backward bifurcation phenomenon and on the basic reproduction number R0. � 2017 NSP. | en_US |
| dc.description.uri | https://www.scimagojr.com/journalsearch.php?q=21100871775&tip=sid&clean=0 | |
| dc.language.iso | English | en_US |
| dc.publisher | Natural Sciences Publishing | en_US |
| dc.relation.ispartofseries | Progress in Fractional Differentiation and Applications | |
| dc.relation.ispartofseries | 3 | |
| dc.subject | Computer virus | en_US |
| dc.subject | Fractional calculus | en_US |
| dc.subject | Numerical solution | en_US |
| dc.subject | Predictor-corrector method | en_US |
| dc.title | Backward bifurcation in a fractional order epidemiological model | en_US |
| dc.type | Article | en_US |
| dcterms.isReferencedBy | (2009) WHO Guide to Identifying the Economic Consequences of Disease and Injury, , Geneva: World Health Organization; Arafa, A.A.M., Rida, S.Z., Khalil, M., A fractional-order model of HIV infection: numerical solution and comparisons with data of patients (2014) Int. J. Biomath, 7 (4); Arafa, A.A.M., Rida, S.Z., Khalil, M., A fractional-order model of HIV infection with drug therapy effect (2014) J. Egypt. Math. Soc, 22, pp. 538-543; Arafa, A.A.M., Rida, S.Z., Khalil, M., The effect of anti-viral drug treatment of human immunodeficiency (2013) Appl. Math. Model, 37, pp. 2189-2196; Arafa, A.A.M., Rida, S.Z., Khalil, M., Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection (2012) Nonlin. Biomed. Phys, 6, pp. 1-7; Arafa, A.A.M., Rida, S.Z., Khalil, M., Fractional order model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+T-cells (2011) Adv. Stud. Biol, 3, pp. 347-353; Ding, Y., Yea, H., A fractional-order differential equation model of HIV infection of CD4+T-cells (2009) Math. Comput. Model, 50, pp. 386-392; Keeling, M.J., Danon, L., Mathematical modelling of infectious diseases (2009) Brit. Med. Bull, 92, pp. 33-42; Rihan, F.A., Numerical modeling of fractional-order biological systems (2013) Abstr. Appl. Anal. 2013; Safan, M., Heesterbeek, H., Dietz, K., The minimum effort required to eradicate infections in models with backward bifurcation (2006) J. Math. Biol, 53, pp. 703-718; Safan, M., Kretzschmar, M., Hadeler, K.P., Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis (2013) J. Math. Biol, 67, pp. 1083-1110; Safan, M., Rihan, F.A., Mathematical analysis of an SIS model with imperfect vaccination and backward bifurcation (2014) Math. Comput. Simul, 96, pp. 195-206; Brauer, F., Backward bifurcations in simple vaccination models (2004) J. Math. Anal. Appl, 298, pp. 418-431; Buonomoland, B., Lacitignola, D., On the backward bifurcation of a vaccination model with nonlinear incidence (2011) Nonlinear Anal. Model. Contr, 16, pp. 30-46; El-Saka, H.A.A., Backward bifurcations in fractional-order vaccination models (2015) J. Egypt. Math. Soc, 23, pp. 49-55; Sharomi, O., Podder, C.N., Gumel, A.B., Elbasha, E.H., Watmough, J., Role of incidence function in vaccine-induced backward bifurcation in some HIV models (2007) Math. Biosci, 210 (2), pp. 436-463; G�mez-Acevedo, H., Li, M.Y., Backward bifurcation in a model for HTLV-I infection of CD4+ T cells (2005) Bull. Math. Biol, 67, pp. 101-114; Lashari, A.A., Hattaf, K., Zaman, G., Li, X.Z., Backward bifurcation and optimal control of a vector borne disease (2013) Appl. Math. Inf. Sci, 71 (1), pp. 301-309; Ahmed, E., El-Sayed, A.M.A., El-Saka, H.A.A., Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models (2007) J. Math. Anal. Appl, 325, pp. 542-553; Ahmed, E., Elgazzar, A.S., On fractional order differential equations model for nonlocal epidemics (2007) Phys. A, 379, pp. 607-614; Abdullah, F.A., Ismail, A.I.M., Simulations of the spread of the Hantavirus using fractional fifferential equations (2011) Matematika, 27, pp. 149-158; Diethelm, K., A fractional calculus based model for the simulation of an outbreak of dengue fever (2013) Nonlinear Dyn, 71, pp. 613-619; El-Misiery, A.E., Ahmed, E., On a fractional model for earthquakes (2006) Appl. Comput. Math, 178, pp. 207-211; Moaddy, K., Radwan, A.G., Salama, K.N., Momani, S., Hashim, I., The fractional-order modeling and synchronization of electrically coupled neuron systems (2012) Comput. Math. Appl, 64, pp. 3329-3339; El-Sayed, A.M., Rida, S.Z., Arafa, A.A.M., On the solutions of time-fractional bacterial chemotaxis in adiffusion gradientchamber (2009) Int. J. Nonlin. Sci. Numer, 7, pp. 485-492; El-Sayed, A.M., El-Mesiry, A.E.M., El-Saka, H.A.A., Numerical solution for multi-term fractional (arbitrary) orders differential equations (2004) Comput. Appl. Math, 23, pp. 33-54; El-Sayed, A.M., El-Kalla, I.L., Ziada, E.A.A., Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations (2010) Appl. Numer. Math, 60, pp. 788-797; El-Sayed, A.M., Rida, S.Z., Arafa, A.A.M., Exact solutions of sometime-fractional biological population models by using generalized differential transform method (2010) Int. J. Math. Model. Simul. Appl, 3, pp. 231-239; Du, M., Wang, Z., Hu, H., Measuring memory with the order of fractional derivative (2013) Sci. Rep, 3, pp. 142-147; El-Sayed, A.M.A., On the existence and stability of positive solution for a nonlinear fractional-order differential equation and some applications (2010) Alex. J. Math, 1, pp. 1-10; Li, C.P., Zhang, F.R., A survey on the stability of fractional differential equations (2011) Eur. Phys. J. Special Topics, 193, pp. 27-47; Lin, W., Global existence theory and chaos control of fractional differential equations (2007) J. Math. Anal. Appl, 332, pp. 709-726; Sardar, T., Rana, S., Bhattacharya, S., Al-Khaled, K., Chattopadhyay, J., A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector (2015) Math. Biosci, 263, pp. 18-36 | |
| dcterms.source | Scopus | |
| dc.identifier.doi | https://doi.org/10.18576/pfda/030404 | |
| dc.Affiliation | October University for modern sciences and Arts (MSA) |
