TY - JOUR AU - Çakan, Ümit PY - 2021 TI - On the stability analysis of solutions of an integral equation with an application in epidemiology JO - Mathematics in Natural Science SP - 16--25 VL - 7 IS - 1 AB - This paper concerns a nonlinear integral equation modeling the spread of epidemics in which immunity does not occur after recovery. The model is mainly based on the return of some of the individuals who have been exposed to the pathogen and who have completed the incubation period, into the susceptible class. We first prove the uniqueness of the global solution of the model with the given initial conditions. After determining the positively invariant region for the model, using LaSalle invariance principle [J. P. LaSalle, IRE Trans. CT, \({\bf 7} (1960)\), 520--527] and the concept of persistence we present some results about the stability analysis of the solutions according to the case of the reproduction number \(\mathcal{R}_{0}\) which is a vital threshold in the spread of diseases. SN - ISSN 2600-7665 UR - http://dx.doi.org/10.22436/mns.07.01.02 DO - 10.22436/mns.07.01.02 ID - Çakan2021 ER - TY - JOUR TI - Stability analysis of an SIR epidemic with non-linear incidence rate and treatment AU - O. Adebimpe AU - K. A. Bashiru AU - T. A. Ojurongbe JO - Open J. Model. Simul. PY - 2015 DA - 2015// VL - 3 ID - Adebimpe2015 ER - TY - JOUR TI - Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative AU - E. Balcı AU - İ. Öztürk AU - S. Kartal JO - Chaos Solitons Fractals PY - 2019 DA - 2019// VL - 123 ID - Balcı2019 ER - TY - JOUR TI - Stability switches induced by immune system boosting in an SIRS model with discrete and distributed delays AU - M. V. Barbarossa AU - M. Polner AU - G. Röst JO - SIAM J. Appl. Math. PY - 2017 DA - 2017// VL - 77 ID - Barbarossa2017 ER - TY - JOUR TI - Global stability of an SIR epidemic model with time delays AU - E. Beretta AU - Y. Takeuchi JO - J. Math. Biol. PY - 1995 DA - 1995// VL - 33 ID - Beretta 1995 ER - TY - JOUR TI - Global asymptotic stability of an SIR epidemic model with distributed time delay AU - E. Beretta AU - T. Hara AU - W. Ma AU - Y. Takeuchi JO - Nonlinear Anal. PY - 2001 DA - 2001// VL - 47 ID - Beretta2001 ER - TY - BOOK TI - Mathematical models in population biology and epidemiology: second edition AU - F. Brauer AU - C. Castillo-Chavez PB - Springer PY - 2012 DA - 2012// CY - New York ID - Brauer2012 ER - TY - JOUR TI - https://www.hindawi.com/journals/ddns/2011/653937/ AU - H. Cao AU - Y. Zhou AU - B. Song JO - Discrete Dyn. Nat. Soc. PY - 2011 DA - 2011// VL - 2011 ID - Cao2011 ER - TY - JOUR TI - A new model for tumor growth analysis based on a postulated inhibitory substance AU - E. B. Cox AU - M. A. Woodbury AU - L. E. Myers JO - Comp. Biomed. Res. PY - 1980 DA - 1980// VL - 13 ID - Cox1980 ER - TY - BOOK TI - Mathematical modelling in economics: Essays in Honor of Wolfgang Eichhorn AU - W. E. Diewert AU - K. Spremann AU - F. Stehling PB - Springer PY - 1993 DA - 1993// CY - Berlin ID - Diewert1993 ER - TY - JOUR TI - Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission AU - P. V. D. Driessche AU - J. Watmough JO - Math. Biosci. PY - 2002 DA - 2002// VL - 180 ID - Driessche2002 ER - TY - JOUR TI - Global analysis of a delay SVEIR epidemiological model AU - N. Farajzadeh Tehrani AU - M. R. Razvan AU - S. Yasaman JO - Iran. J. Sci. Technol. Trans. A Sci. PY - 2013 DA - 2013// VL - 37 ID - Tehrani2013 ER - TY - BOOK TI - Fractional-order viscoelasticity (FOV): Constitutive developments using the fractional calculus: First annual report AU - A. D. Freed AU - K. Diethelm AU - Y. Luchko PB - Technical Memorandum, TM-2002-211914, NASA Glenn Research Center PY - 2002 DA - 2002// CY - Cleveland ID - Freed2002 ER - TY - JOUR TI - A mathematical model of Hepatitis B transmission in Turkey AU - M. Golgeli JO - Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. PY - 2019 DA - 2019// VL - 68 ID - Golgeli2019 ER - TY - JOUR TI - On some epidemic models AU - G. Gripenberg JO - Quart. Appl. Math. PY - 1981 DA - 1981// VL - 39 ID - Gripenberg1981 ER - TY - JOUR TI - Integral equation models for endemic infectious diseases AU - H. W. Hethcote AU - D. W. Tudor JO - J. Math. Biol. PY - 1980 DA - 1980// VL - 9 ID - Hethcote1980 ER - TY - JOUR TI - Integral equations arising in the kinetic theory of gases AU - S. Hu AU - M. Khavanin AU - W. Zhuang JO - Appl. Anal. PY - 1989 DA - 1989// VL - 34 ID - Hu1989 ER - TY - JOUR TI - A contribution to the mathematical theory of epidemics AU - W. O. Kermack AU - A. G. McKendrick JO - Part I Proc. Roy. Soc. A PY - 1927 DA - 1927// VL - 115 ID - Kermack1927 ER - TY - JOUR TI - Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators AU - I. Koca JO - Eur. Phys. J. Plus PY - 2018 DA - 2018// VL - 133 ID - Koca2018 ER - TY - JOUR TI - Lyapunov functions and global properties for SEIR and SEIS epidemic models AU - A. Korobeinikov JO - Math. Med. Biol. PY - 2004 DA - 2004// VL - 21 ID - Korobeinikov2004 ER - TY - BOOK TI - Delay differential equations: with applications in population dynamics AU - Y. Kuang PB - Academic Press PY - 1993 DA - 1993// CY - Boston ID - Kuang1993 ER - TY - JOUR TI - Some extensions of Liapunov’s second method AU - J. P. LaSalle JO - IRE Trans. CT PY - 1960 DA - 1960// VL - 7 ID - LaSalle1960 ER - TY - JOUR TI - The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission AU - Z. Lu AU - X. Chi AU - L. Chen JO - Math. Comput. Modelling PY - 2002 DA - 2002// VL - 36 ID - Lu2002 ER - TY - JOUR TI - Global stability of an SIR epidemic model with time delay AU - W. Ma AU - M. Song AU - Y. Takeuchi JO - Appl. Math. Lett. PY - 2004 DA - 2004// VL - 17 ID - Ma2004 ER - TY - JOUR TI - Permanence of an SIR epidemic model with distributed time delays AU - W. Ma AU - Y. Takeuchi AU - T. Hara AU - E. Beretta JO - Tohoku Math. J. PY - 2002 DA - 2002// VL - 54 ID - Ma2002 ER - TY - JOUR TI - Complete global stability for an SIR epidemic model with delay distributed or discrete AU - C. C. McCluskey JO - Nonlinear Anal. Real World Appl. PY - 2010 DA - 2010// VL - 11 ID - McCluskey2010 ER - TY - JOUR TI - Lyapunov functions and global properties of SEIR epidemic model AU - M. M. Ojo AU - F. O. Akinpelu JO - IJCMP PY - 2017 DA - 2017// VL - 1 ID - Ojo2017 ER - TY - JOUR TI - Stability analysis susceptible, exposed, infected, recovered (SEIR) model for spread model for spread of dengue fever in medan AU - S. Side AU - Y. M. Rangkuti AU - D. G. Pane AU - M. S. Sinaga JO - J. Phys.: Conf. Ser. PY - 2018 DA - 2018// VL - 954 ID - Side2018 ER - TY - JOUR TI - Dynamical systems and population persistence AU - H. L. Smith AU - H. R. Thieme JO - American Mathematical Society, PY - 2011 DA - 2011// VL - 118 ID - Smith2011 ER - TY - JOUR TI - On the appearance of the fractional derivative in the behavior of real materials AU - P. J. Torvik AU - R. L. Bagley JO - J. Appl. Mech. PY - 1984 DA - 1984// VL - 51 ID - Torvik1984 ER - TY - JOUR TI - Stochastic dynamics of an SEIS epidemic model AU - B. Yang JO - Adv. Difference Equ. PY - 2016 DA - 2016// VL - 226 ID - Yang2016 ER -