References
- Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc Roy Soc A. 1927;115:700–721. doi:10.1007/BF02464423
- Affandi P, Faisal. Optimal control mathematical SIR model of malaria spread in south Kalimantan. IOP Conf Ser J Phys Conf Series. 2018;1116:022001. doi:10.1088/1742-6596/1116/2/022001
- Misra AK, Singh V. A delay mathematical model for the spread and control of water borne diseases. J Theor Biol. 2012;301:49–56. doi:10.1016/j.jtbi.2012.02.006
- Barlow NS, Weinstein SJ. Accurate closed-form solution of the SIR epidemic model. Phys D. 2020;408:132540. doi:10.1016/j.physd.2020.132540
- Chekroun A, Kuniya T. An infection age-space structured SIR epidemic model with Neumann boundary condition. Appl Anal. 2020;99(11):1972–1985. doi:10.1080/00036811.2018.1551997
- Cooper I, Mondal A, Antonopoulos CG. A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solit Fractals. 2020;139:110057. doi:10.1016/j.chaos.2020.110057
- Rajasekar SP, Pitchaimani M. Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence. Appl Math Comput. 2020;377:125143 15 pp. doi:10.1016/j.amc.2020.125143
- Sharov KS. Creating and applying SIR modified compartmental model for calculation of COVID-19 lockdown efficiency. Chaos, Solit Fractals. 2020;141:110295. doi:10.1016/j.chaos.2020.110295
- Slama H, Hussein A, El-Bedwhey NA, et al. An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique. Appl Math Comput. 2019;361:144–156. doi:10.1016/j.amc.2019.05.019
- Volpert V, Banerjee M, Petrovskii S. On a quarantine model of coronavirus infection and data analysis. Math Model Nat Phenom. 2020;15:24. doi:10.1051/mmnp/2020006
- Wang Z, Guo Q, Sun S, et al. The impact of awareness diffusion on SIR-like epidemics in multiplex networks. Appl Math Comput. 2019;349:134–147. doi:10.1016/j.amc.2018.12.045
- Brauer F, Castillo-Chavez C. Mathematical models in population biology and epidemiology. New York, NY: Springer; 2001. ISBN:0-387-98902-1.
- Chen L, Chen J. Nonlinear dynamical systems of biology. Beijing: Science; 1993 [in Chinese].
- Diekmann O, Heesterbeek JAP. Mathematical epidemiology of infectious diseases. Chichester, UK: John Wiley Sons; 2000. ISBN: 0-471-49241-8.
- Zeng GZ, Chen LS, Sun LH. Complexity of an SIR epidemic dynamics model with impulsive vaccination control. Chaos Solit Fractals. 2005;26:495–505. doi:10.1016/j.chaos.2005.01.021
- Liu WM, Levin SA, Lwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J Math Biol. 1986;23;(2):187–204. doi:10.1007/BF00276956
- Liu WM, Hethcote HW, Levin SA. Dynamical behavior of epidemiological models with nonlinear incidence rates. J Math Biol. 1987;25:359–380. doi:10.1007/BF00277162
- Wang H. Existence of Hopf bifurcation periodic solution to SIRS epidemiological models with nonlinear incidence rates. J Anhui Agric Univ. 2002;29(2):199–202. (in Chinese).
- Dumortier F, Llibre J, Artés JC. Qualitative theory of planar differential systems. New York: UniversiText, Springer–Verlag; 2006. ISBN: 3-540-32893-9.
- Kuznetzov YA. Elements of applied bifurcation theory. 2nd ed., New York; Springer; 1998. (Appl Math Sci; 112). ISBN: 0-387-98382-1.