% دستوراتی برای به حالت عادی درآمدن اندازه فونت‌ها و فاصله بین خطوط
\normalsize
\renewcommand{\baselinestretch}{2}

% مراجع خود را در این قسمت وارد کنید
%\begin{thebibliography}{99}
% چنانچه از نسخه‌های قدیمی زی‌پرشین استفاده می‌کنید، هنگام استفاده از دستورهای


%\setLTRbibitems
\begin{thebibliography}{99}
\begin{RTLbibitems}
%\begin{Persian}
%\Persian


	\bibitem{kiani}
	 شمیسا عبدالله ، کیانی  زهرا، سیستم‌های کنترل بهینه، تهران: نیاز دانش، 1392
	\bibitem{amin}
	محمدزاده احسان، پریز ناصر، حسینی ثانی سیدکمال، جاجرمی امین، کنترل بهینه دسته‌ای از سیستم‌های غیرخطی مرتبه کسری بااستفاده از سری مودال توسعه‌یافته و استراتژی برنامه‌ریزی خطی،کنترل، 2016

%\bibitem{Watkinsp}
%\end{Persian}
\end{RTLbibitems}
%\begin{LTRbibitems}
%\resetlatinfont

%\begin{latin}1392
\latin

\bibitem{ahmad} AHMAD, S. and RAO, M.R.M.,  \textit{Theory of Ordinary Differential Equations with Applications in Biology and Engineering.} Affiliated East-West Press
Pvt. Ltd, New Delhi, 1999. 

\bibitem{agrawal} AGRAWAL, O.P., "A general formulation and solution scheme for fractional optimal control problems," \textit{Nonlinear Dynamics} \textbf{38} (2004)  323--337.

\bibitem{agrawal2008}  AGRAWAL, O. P., "A quadratic numerical scheme for fractional optimal control problems," \textit{Dynamic Systems, Measurement, and Control,} \textbf{130} (2008) no. 1, 1-9

\bibitem{baba}  BABA,B. A. and BILGEHAN, B. "Optimal control of a fractional order model for the COVID--19 pandemic," \textit{Chaos, Solitons \& Fractals,} \textbf{144} (2023) 110678.

\bibitem{baleanu} BALEANU, D., HASANABADI, M., VAZIRI, A. and JAJARMI, A., "A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach," \textit{Chaos, Solitons \& Fractals,} \textbf{167} (2023) 113078.

\bibitem{bandeira} BANDEIRA, T., CARMO, M., LOPES, H., GOMES, C. and et al., "Burden and severity of children's hospitalizations by respiratory syncytial virus in Portugal, 2015--2018," \textit{Influenza and Other Respiratory Viruses,} \textbf{17} (2023)  no. 1, e13066.
	
\bibitem{barry} BARRY, M., TRAOR{\'E}, F. A., SAKO, F.B., KPAMY, D. O., BAH, E. I., PONCIN, M., KEITA, S., CISSE, M. and TOUR{\'E}, A., "Ebola outbreak in Conakry, Guinea: epidemiological, clinical, and outcome features," \textit{Medecine et maladies infectieuses} \textbf{44} (2014) no. 11, 491--494.

\bibitem{brannstrom} BR{\"A}NNSTR{\"O}M, {\AA}. and SUMPTER, D. J. T., "The role of competition and clustering in population dynamics," \textit{Proceedings of the Royal Society B: Biological Sciences} \textbf{272} (2005) no. 1576, 2065--2072.

\bibitem{berge}  BERGE, C. T., LUBUMA, J. M.-S., MOREMEDI, G. M.,  MORRIS, N. and KONDERA-SHAVA,  R., "A simple mathematical model for Ebola in Africa," \textit{IBM Journal of Research and Development} \textbf{11} (2017) no. 1, 42--74.

\bibitem{bernoulli} BERNOULLI, D., "R{\'e}flexions sur les avantages de l’inoculation," \textit{M{\'e}m. Paris}  \textbf{16} (1758), 439--482.

\bibitem{bibby} BIBBY, K., CASSON, L. W., STACHLER, E. and HAAS, C. N., "Ebola virus persistence in the environment: state of the knowledge and research needs," \textit{Environmental Science \& Technology Letters} \textbf{2} (2015) no. 1, 2--6.

\bibitem{budd}  BUDD, W.,  "Typhoid fever its nature, mode of spreading, and prevention," \textit{American Journal of Public Health} \textbf{8} (1918) no. 8, 610--612.

\bibitem{bouhali} BOUHALI, A., ARIBI,W. B., MILED,S. B. and KEBIR, A., "Optimal Control applied to SIRD model of COVID 19," \textit{arXiv preprint arXiv}, (2021)

\bibitem{cacho}  CACHO, F., GEBRETSADIK, T., ANDERSON,, L. J.,  ChAPPELL, J. D., ROSAS-SALAZAR, C. O., JUSTON, R. O. and HARTERT, T., "Respiratory Syncytial Virus Prevalence and Risk Factors among Healthy Term Infants, United States," \textit{merging Infectious Diseases} \textbf{30} (2024)  no. 10, 2199.

\bibitem{Capasso} CAPASSO, V., " Mathematical structure of the epidemic systems," In \textit{Biomathematics}, Springer-Verlag, Berlin, Heidelberg, \textbf{97} 1993.

\bibitem{chou2016introduction} CHOU, S. C. and FRIEDMAN, A.,  \textit{Introduction to mathematical biology: modeling, analysis, and simulations.} Springer,  2016. 

\bibitem{chowell}  CHOWELL, G., VIBOUD, C., HYMAN, J. M. and SIMONSEN, L., "The Western Africa Ebola virus disease epidemic exhibits both global exponential and local polynomial growth rates," \textit{PLoS currents} \textbf{7} (2015).

\bibitem{drazin} DRAZIN, P. G., \textit{Nonlinear systems.} Cambridge University Press, \textbf{5} 1992.

\bibitem{delves}  DELVES, L. M. and MOHAMED, J. L.,  \textit{Computational Methods for Integral Equations.} CUP Archive ,1985.

\bibitem{diekmann2000mathematical} DIEKMAN, O. and HEESTERBEEK, J. A. P. \textit{Mathematical epidemiology of infectious diseases: model building, analysis and interpretation.} John Wiley \& Sons,  \textbf{5} 2000.

\bibitem{diekmann} DIEKMAN, O., HEESTERBEEK, J. A. P. and METZ, J. A. J, "On the definition and the computation of the basic reproduction ratio $ R_0 $ in models for infectious diseases in heterogeneous populations," \textit{Journal of mathematical biology} \textbf{28} (1990) 365--382.

\bibitem{diethelm} DIETHELM, K., \textit{The Analysis of Fractional Differential Equations.} Springer-Verlag, 2010.

\bibitem{diethelm1} DIETHELM, K., "The Analysis of Fractional Diferential Equations: An Application-Oriented Exposition Using Operators of Caputo Type," \textit{Springer} (2004). 

\bibitem{diethelm2} DIETHELM K. and FORD, N.J., "Analysis of fractional differential equations," \textit{ J Math Anal Appl} \textbf{265} (2002) no. 2, 229–48.

\bibitem{djiomba} DJIOMBA NJANKOU, S. D. and NYABADZA, F., "Modelling the role of human behaviour in Ebola virus disease (EVD) transmission dynamics," \textit{Computational and Mathematical Methods in Medicine} \textbf{2022} (2022) no. 2, 4150043.

\bibitem{djiomba2} DJIOMBA NJANKOU, S. D. and NYABADZA, F.,  "Modelling the potential role of media campaigns in Ebola transmission dynamics," \textit{International Journal of Differential Equations} \textbf{2017} (2017) no. 1, 3758269.

\bibitem{duarte} DUARTE-MERMOUD, M. A., AGUILA-CAMACHO, N., GALLEGOS, J. A. and CASTRO, L. R., "Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems," \textit{Communications in Nonlinear Science and Numerical Simulation} \textbf{22} (2015) no. 1--3, 650--659.

\bibitem{Evirgen} EVIRGEN, F., "Transmission of {N}ipah virus dynamics under {C}aputo fractional derivative," \textit{Journal of Computational and Applied Mathematics} \textbf{418} (2023) , 114654.

\bibitem{farr} FARR, W.,  "Progress of epidemics. 2-d Report of the regist. general of England and Wales," \textit{London [in English]} (1840) .

\bibitem{Gantmacher} GANTMACHER, F. R.,  "The theory of matrices. {V}ol. 2," \textit{Chelsea Publishing Co., New York} (1959) .

\bibitem{graunt1939natural} GRAUNT, J. and WILLCOX, W. F., \textit{Natural and political observations made upon the bills of mortality.} Hassell Street Press, London
 (1939).
 
 \bibitem {garrappa} GARRAPA, R., "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," \textit{Mathematics and Computers in Simulation} \textbf{110} (2015) 96--112.
 
 \bibitem{hackbush} HACKBUSH, W., "A numerical method for solving parabolic equations with opposite orientations," \textit{Computing}  \textbf{20} (1978) no. 3, 229--240.
 
 \bibitem{Harcourt} HARCOURT, B. H., LOWE, L., TAMIN, A., et al., "Genetic characterization of Nipah virus, Bangladesh, 2004," \textit{Emerging Infect Dis}  \textbf{11} (2005) no. 10, 1594.
 
 \bibitem{haykin} HAYKIN, S., "Neural networks: a comprehensive foundation." Prentice Hall PTR, Upper Saddle River, New Jersey, USA  1998.

\bibitem{hethcote} HETHCOTE, H. W.,  "The mathematics of infectious diseases," \textit{SIAM review} \textbf{44} (2000) no. 4, 599--653.

\bibitem{henao} HENAO-RESTREPO, A. M. and et al. ,"Efficacy and effectiveness of an rVSV-vectored vaccine expressing Ebola surface glycoprotein: interim results from the Guinea ring vaccination cluster-randomised trial," \textit{The Lancet}  \textbf{386} (2015) no. 9996, 857--866.

\bibitem{heesterbeek} HEESTERBEEK, J. and DIETZ, K.,  "The concept of $ R_{0} $ in epidemic theory," \textit{Statistica neerlandica} \textbf{50} (1996) no. 1, 89--110.

\bibitem{kaler}  KALER, J., AZHAR, H., KISHAN, P., HERNANDEZ, T. and RAY, S., "Respiratory syncytial virus: A comprehensive review of transmission, pathophysiology, and manifestation," \textit{Cureus} \textbf{15} (2023)  no. 3.

\bibitem{khan}  KHAN, M. Y., ULLAH, S., FAROOQ, M., Al AlWAN, B., SAQIB, A. B., "Optimal control analysis for the Nipah infection with constant and time-varying vaccination and treatment under real data application," \textit{Scientific Reports}, \textbf{14} (2024) no.1, 17532.
	
\bibitem{khamsi} KHASMI, M. A., KIRK, W. A., \textit{An introduction to metric spaces and fixed point theory,} John Wiley \& Sons, 2011.
	
\bibitem{legrand} LEGRAND, J.,  GRAIS, R. F., BOELLE, P. Y.,  VALLERON, A. J., FLAHAULT, A., "Understanding the dynamics of Ebola epidemics," \textit{Epidemiology \& Infection} \textbf{153} (2007) no. 4, 610--621.

\bibitem{lekone} LEKONE, P. E. and FINKENST{\"A}DT, B. F., "Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study," \textit{Biometrics} \textbf{62}  (2006) no. 4, 1170--1177.

\bibitem{levins} LEVINS, R., AWERBUCH, T., BRINKMANN, U., ECKARDT, I., EPSTEIN, P., MAKHOUL, N., DE POSSAS, C.A., PUCCIA, C., SPIELMAN, A. and WILSON, M.E., "The emergence of new
diseases," \textit{American Scientist}  \textbf{82} (1994) no. 1, 52--60.

\bibitem{li} LI, Y., CHEN, Y. Q. and PODLUNNY, I., "Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag--Leffler stability," \textit{Computers \& Mathematics with Applications} \textbf{59} (2010) no. 5, 1810--1821.

\bibitem{liu} LIU, Y., ROBERTS, J. and YAN, Y., "Detailed error analysis for a fractional Adams method with graded meshes," \textit{ Numerical Algorithms} \textbf{78} (2018) 1195--1216.

\bibitem{lobanov}  LOBANOV, S. G. and SMOLYANOV, O. G., "Ordinary differential equations in locally convex spaces," \textit{Russian Mathematical Surveys} \textbf{49} (1994) no. 3, 97.

\bibitem{marchuk2013mathematical} MARCHUCK, G. I.,  \textit{Mathematical modelling of immune response in infectious diseases.} Springer Science \& Business Media,  \textbf{395} 2013. 

\bibitem{mcasey}  MCASEY, M., MOU, L. and HAN, W., "Convergence of the forward-backward sweep method in optimal control," \textit{Computational Optimization and Applications} \textbf{53} (2012) 207--226.

\bibitem{mitra} MITRA, A., "Modified $ SIRD $ Model of Epidemic Disease Dynamics: A case Study of the COVID-19 Coronavirus," \textit{J. Mech. Cont. \& Math. Sci} \textbf{16} (2021) no. 2, 1--8.

\bibitem{monje} MONJE, C. A., CHEN, Y., VINAGRE, B. M., XUE, D. and FELIU-BATLLE, V., \textit{Fractional-order systems and controls: fundamentals and applications.} Springer Science \& Business Media, 2010.

\bibitem{mondal} MONDAL, M., K., HANIF, M. and BIWAS M. H. A., "A mathematical analysis for controlling the spread of Nipah virus infection," \textit{Journal of mechanics of continua and mathematical sciences} \textbf{37} (2017) no. 3, 185–97.

\bibitem{muhammad} MUHAMMAD, A. K. and ATANGANA, A., "Dynamics of Ebola disease in the framework of different fractional derivatives," \textit{Entropys} \textbf{21} (2019) no. 3, 303.

\bibitem{odibat} ODIBAT, Z. M. and SHAWAGFEH, N. T. ,"Generalized Taylor’s formula," \textit{Applied Mathematics and computation}  \textbf{186} (2007) no. 1, 286--293.

\bibitem{podlubny} PODLUNNY, I., \textit{Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications,} elsevier, 1998.

\bibitem{pontryagin} PONTRYAGIN, L. S., \textit{Mathematical theory of optimal processes.} Interscience Publishers (John Wiley \& Sons), New York, 1987.

\bibitem{pooseh} POOSEH, S., ALMEIDA, R. and TORRES, D. F. M., "Fractional order optimal control problems with free terminal time," \textit{arXiv preprint arXiv:1302.1717} (2013).

\bibitem{rabiei}  RABIEI, K., ORDOKHANI, Y.and BABOLIAN, E., "The Boubaker polynomials and their application to solve fractional optimal control problems," \textit{Nonlinear Dynamics} \textbf{88} (2017) 1013-1026.

\bibitem{raza}  RAZA, A., AWREJCEWICZ, J., RAFIQ, M. and MOHSIN, M., "Breakdown of a nonlinear stochastic nipah virus epidemic models through efficient numerical methods," \textit{Entropy} \textbf{23} (2021) no. 12, 1588.

\bibitem{rosa}  ROSA, S. and NDA{\"I}ROU, F., "Optimal Control Applied to Piecewise-Fractional Ebola Model," \textit{Mathematics} \textbf{12} (2024) no. 7, 985.

\bibitem{rosa20} Rosa, S. and Torres., D. F. M., "Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection," \textit{Chaos, Solitons \& Fractals} \textbf{117} (2018) 142--149.

\bibitem{saeedian} SAEEDIAN, M., KHALIGHI, M., AZIMI, N., JAFARI, G. R. and AUSLOOS, M., "Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model," \textit{Physical Review E} \textbf{95} (2017) no. 2, 022409.

\bibitem{Sayevand} SAYEVAND, K. and ROSTAMI, M., "Fractional optimal control problems: optimality conditions and numerical solution," \textit{IMA Journal of Mathematical Control and Information} \textbf{35} (2018) no. 1, 123--148.

\bibitem{shekari1}  BALEANU, D., SHEKARI, P., TORKZADEH, L., RANJBAR, H., JAJARMI, A. and NOURI, K., "Stability analysis and system properties of Nipah virus transmission: A
fractional calculus case study," \textit{Chaos, Solitons \& Fractals} \textbf{166} (2023) 112990.

\bibitem{shekari} SHEKARI, P., JAJARMI, A., TORKZADEH, L. and NOURI, K., "Fractional-order modeling of human behavior in infections: analysis using real data from Liberia," \textit{Computer Methods in Biomechanics and Biomedical Engineering}  (2025) 1--15.

\bibitem{slotine} SLOTINE, J. E. and LI, W., \textit{Applied nonlinear control.} Prentice hall, Englewood Cliffs, New Jersey, \textbf{199} 1991.

\bibitem{shah}  SHAH, N. H., SUTHAR, A. H., THAKKAR, F. A. and SATIA, M. H., "SEI-model for transmission of Nipah virus," \textit{Journal of Mathematics and Computer Science} \textbf{8} (2018) no. 6, 714--730.

\bibitem{snow} SNOW, J.,  \textit{On the mode of communication of cholera.} John Churchill, New Burlington Street, London,  1855. 

\bibitem{sriram} SRIRAM, N. and PRASAD, C. R., "An Overview of Ebola virus Disease (EVD) or Ebola hemorrhagic fever (EHF)," \textit{Optimization Methods and Software} \textbf{2} (2014) no. 4, 269--278.

\bibitem{sun} SUN, H. G., CHEN, W., WEI, H. and CHEN, Y. Q., "A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems," \textit{The european physical journal special topics} \textbf{193} (2011) no. 1, 185--192.

\bibitem{sultana} SULTANA, J. and PODDER, C. N., "Mathematical analysis of Nipah virus infections using optimal control theory," \textit{Journal of Applied Mathematics and Physics} \textbf{4} (2016) no. 6, 1099--1111.

\bibitem{taylor} TALOR, L. H., LATHAM, S. M. and WOOLHOUSE, M. E. J., "Risk factors for human disease emergence," \textit{Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences}  \textbf{356} (2001) no. 1411, 983--989.

\bibitem{tottori} TOTTORI, T. and KOBAYASHI, T. J., "Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control," \textit{Entropy}  \textbf{25} (2023) no. 2, 208.

\bibitem{ullah} ULLAH, S., NAWAZ, R., AlQAHTANI, A. S., LI, S. and HASSAN,  A. M., "A mathematical study unfolding the transmission and control of deadly Nipah virus infection under optimized preventive measures: New insights using fractional calculus," \textit{Results in Physics}, \textbf{51} (2023) 106629.

\bibitem{ustun} {\"U}ST{\"U}N, {\c{C}}. and {\"O}ZG{\"U}RLER, {\"O}., "Ebola: A significant threat as an infectious disease, and as a potential bioterrorism agent," \textit{Turkish Journal of Medical Sciencess} \textbf{35} (2005) no. 1, 1--4.

\bibitem{vargas}  VARGAS-DE-LE{\'O}N, C., "Volterra-type Lyapunov functions for fractional-order epidemic systems," \textit{Communications in Nonlinear Science and Numerical Simulation} \textbf{24} (2015) no. 1--3, 75--85.

\bibitem{vitanov} VITANOV, N. K. and AUSLOOS, M. R., "Knowledge epidemics and population dynamics models for describing idea diffusion,Models of science dynamics: Encounters between complexity theory and information sciences" \textit{Springer Verlag, Berlin Heidelberg} (2011) Ch. 3, 69--125.


\bibitem{world}  WORLD HEALTH ORGANIZARION, "Ebola and Marburg virus disease epidemics: preparedness, alert, control, and evaluation," \textit{World Health Organization} ( 2014).

\bibitem{yang} YANG, J. X., "A $ SIRD $ epidemic model with community structure," \textit{Chaos: An Interdisciplinary Journal of Nonlinear Science} \textbf{31} (2021) no. 1.

\bibitem{zewdie}  ZEWIDE, A. D. and GAKKAR, S., "A mathematical model for Nipah virus infection," \textit{Journal of Applied Mathematics} \textbf{20} (2020) no. 1, 6050834.

%\bibitem{1} N. Andrei. Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization. European J. Oper. Res., 204(3):410–420, 2010.
















%\bibitem{AminifardBabaieNA} BABAIE--KAFAKI, S. and AMINIFARD, Z., ``Two--parameter scaled memoryless BFGS methods with a nonmonotone choice for the initial step length," \textit{Numer. Algorithms} (2019) DOI: 10.1007/s11075-019-00658-1.


%








%
%\bibitem{BabaieGhanbari4OR} S. Babaie–Kafaki and R. Ghanbari. A class of adaptive {D}ai--{L}iao conjugate gradient methods based on the scaled memoryless {BFGS} update}. 4OR, DOI: 10.1007/s10288--016--0323--1, 2016.
%

%
%\bibitem{BabaieGhanbariJIMO} S. Babaie–Kafaki and R. Ghanbari. A class of descent four--term extension of the {D}ai--{L}iao conjugate gradient method based on the scaled memoryless {BFGS} update. J. Ind. Manag. Optim., DOI: 10.3934/jimo.2016038, 2016.






%\bibitem{BabaieGhanbariOL} S. Babaie–Kafaki and R. Ghanbari. Two modified three–term conjugate gradient methods with sufficient descent property. Optim. Lett., 8(8):2285–2297, 2014.
%
%\bibitem{SBK4OR} BABAIE-KAFAKI, S., ``A modified scaled memoryless BFGS preconditioned conjugate gradient method for unconstrained optimization," \textit{4OR} \textbf{11} (2013) no. 4, 361--374.





 














%







%\bibitem{ZhangZhouLiIMA} ZHANG, L., ZHOU, W. and LI, D.H., ``A descent modified Polak–Ribi`ere–Polyak conjugate gradient method and its global convergence,'' \textit{ IMA J. Numer. Anal.} \textbf{26} (2006) no. 4, 629--640.
%\end{latin}
%\end{LTRbibitems}
\end{thebibliography}

