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1.  Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt 
2.  Department of Statistics and Modelling Science, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom 
[1] 
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595607. doi: 10.3934/mbe.2007.4.595 
[2] 
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 14551474. doi: 10.3934/mbe.2013.10.1455 
[3] 
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems  B, 2013, 18 (1) : 3756. doi: 10.3934/dcdsb.2013.18.37 
[4] 
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (12) : 67716782. doi: 10.3934/dcdsb.2019166 
[5] 
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID19: A case study of India, Brazil and Peru. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2021170 
[6] 
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239259. doi: 10.3934/mbe.2009.6.239 
[7] 
Ling Xue, Caterina Scoglio. Networklevel reproduction number and extinction threshold for vectorborne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565584. doi: 10.3934/mbe.2015.12.565 
[8] 
Shuo Zhang, Guo Lin. Propagation dynamics in a diffusive SIQR model for childhood diseases. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021183 
[9] 
P.E. Kloeden, Desheng Li, Chengkui Zhong. Uniform attractors of periodic and asymptotically periodic dynamical systems. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 213232. doi: 10.3934/dcds.2005.12.213 
[10] 
Toshikazu Kuniya, Mimmo Iannelli. $R_0$ and the global behavior of an agestructured SIS epidemic model with periodicity and vertical transmission. Mathematical Biosciences & Engineering, 2014, 11 (4) : 929945. doi: 10.3934/mbe.2014.11.929 
[11] 
Karl Kunisch, Markus Müller. Uniform convergence of the POD method and applications to optimal control. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 44774501. doi: 10.3934/dcds.2015.35.4477 
[12] 
Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a sizestructured population model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 831840. doi: 10.3934/dcdsb.2017041 
[13] 
Liumei Wu, Baojun Song, Wen Du, Jie Lou. Mathematical modelling and control of echinococcus in Qinghai province, China. Mathematical Biosciences & Engineering, 2013, 10 (2) : 425444. doi: 10.3934/mbe.2013.10.425 
[14] 
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 19091927. doi: 10.3934/dcdsb.2013.18.1909 
[15] 
Artur Avila, Thomas Roblin. Uniform exponential growth for some SL(2, R) matrix products. Journal of Modern Dynamics, 2009, 3 (4) : 549554. doi: 10.3934/jmd.2009.3.549 
[16] 
Hisashi Inaba. The Malthusian parameter and $R_0$ for heterogeneous populations in periodic environments. Mathematical Biosciences & Engineering, 2012, 9 (2) : 313346. doi: 10.3934/mbe.2012.9.313 
[17] 
Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostattype model with antibiotic. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 789795. doi: 10.3934/dcdsb.2004.4.789 
[18] 
Xiaorui Wang, Genqi Xu. Uniform stabilization of a wave equation with partial Dirichlet delayed control. Evolution Equations & Control Theory, 2020, 9 (2) : 509533. doi: 10.3934/eect.2020022 
[19] 
Sergey Zelik. Strong uniform attractors for nonautonomous dissipative PDEs with non translationcompact external forces. Discrete & Continuous Dynamical Systems  B, 2015, 20 (3) : 781810. doi: 10.3934/dcdsb.2015.20.781 
[20] 
Mihaï Bostan. Asymptotic behavior for the VlasovPoisson equations with strong uniform magnetic field and general initial conditions. Kinetic & Related Models, 2020, 13 (3) : 531548. doi: 10.3934/krm.2020018 
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