Dynamics of a time-delayed two-strain epidemic model with general incidence rates

Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation

“… and are the transmission rates of strain 1 and strain 2 respectively. We consider because the new strain is highly transmissible ( Farah et al., 2021 ; Khyar & Allali, 2020 ). We also demonstrate the dynamics for the opposite scenario.…”

“…Simply put, this show portrays how ailment voyages in individuals from the susceptible compartment (S) to the infected compartment (I) and after that to the recovered compartment (R), where individuals construct insusceptibility to reinfection. Exposed (E), quarantine (Q), hospitalized (H), and asymptomatic (A) compartments can be used in some epidemics to adequately examine disease dynamics ( Ma et al., 2002 ; Barro et al., 2018 ; Xia et al., 2018 ; Epstein et al., 2021 ; Amador, Armesto, & Gómez-Corral, 2019 ; De León, Avila-Vales, & lin Huang, 2022 ; Amaral, Oliveira, & Javarone, 2021 ; Kabir, Risa, & Tanimoto, 2021 ; M. et al., 2005 ; Meskaf, Khyar, Danane, & Allali, 2020 ; Farah, Amine, & Allali, 2021 ; Dong, Li, Wan, & Liu, 2017 ; Li, Wang, Xu, & Rong, 2022 ; Khyar & Allali, 2020 ; Li, Liu, & Martcheva, 2010 ; Lazebnik & Bunimovich-Mendrazitsky, 2022 ; Beretta & Breda, 2011 ; Rihan, Alsakaji, & Rajivganthi, 2020 ; Khan, Ikram, Din, Humphries, & Akgul, 2021 ; Niño-Torres, Ríos-Gutiérrez, Arunachalam, Ohajunwa, & Seshaiyer, 2022 ; Zuo, Zhu, & Ling, 2022 ; Li & Liu, 2014 ). Examination of supervision and moderation measures, like immunization, establishing of vector-borne maladies, and the impact of birthing and passing elements is an extra application of compartmental models in the study of disease transmission ( Dashtbali & Mirzaie, 2021 ; De León et al., 2022 ; Deka & Bhattacharyya, 2022 ; Epstein et al., 2021 ; Han & Li, 2022 ; Helbing et al., 2015 ; Jusup et al., 2022 ; Kabir et al., 2021 ; Lobinska, Pauzner, Traulsen, Pilpel, & Nowak, 2022 ; Nakata & Omori, 2015 ; Rajib Arefin et al., 2019 ; Tchoumi & Tchuenche, 2021 ; Tori & Tanimoto, 2022 ; Yin, Wang, Xia, & Bauch, 2022 ; Zuo, Zhu, & Ling, 2022 ).…”

“…However, compared to investigations of the dynamical behaviors of multistrain epidemic models with vaccination and time delays, early studies have received little attention. The dynamics of a two-strain epidemic model were studied in ( Rajib Arefin et al., 2019 ; De León et al., 2022 ; M. et al., 2005 ; Meskaf et al., 2020 ; Farah et al., 2021 ; Li et al., 2022 ; Khyar & Allali, 2020 ; Li et al., 2010 ; Lazebnik & Bunimovich-Mendrazitsky, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang, Chen, & Liu, 2016 ; Theprungsimankul, Junsank, Abdulloh, & Chinviriyasit, 2011 ; Khatua, Pal, & Kar, 2014 ; Allali & Amine, 2022 ; Li, Zhang, & Zhou, 2020 ). Epidemic models with time delay were studied in ( Barro et al., 2018 ; Beretta & Breda, 2011 ; Dong et al., 2017 ; Farah et al., 2021 ; Ma et al., 2002 ; Nakata & Omori, 2015 ; Nastasi, Perrone, Taffara, & Vitanza, 2022 ; Yang et al., 2016 ; Yang & Zhang, 2012 ).…”

“…The dynamics of a two-strain epidemic model were studied in ( Rajib Arefin et al., 2019 ; De León et al., 2022 ; M. et al., 2005 ; Meskaf et al., 2020 ; Farah et al., 2021 ; Li et al., 2022 ; Khyar & Allali, 2020 ; Li et al., 2010 ; Lazebnik & Bunimovich-Mendrazitsky, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang, Chen, & Liu, 2016 ; Theprungsimankul, Junsank, Abdulloh, & Chinviriyasit, 2011 ; Khatua, Pal, & Kar, 2014 ; Allali & Amine, 2022 ; Li, Zhang, & Zhou, 2020 ). Epidemic models with time delay were studied in ( Barro et al., 2018 ; Beretta & Breda, 2011 ; Dong et al., 2017 ; Farah et al., 2021 ; Ma et al., 2002 ; Nakata & Omori, 2015 ; Nastasi, Perrone, Taffara, & Vitanza, 2022 ; Yang et al., 2016 ; Yang & Zhang, 2012 ). Multistrain models with vaccination behaviors were studied in ( Rajib Arefin et al., 2019 ; Zuo, Zhu, Meng, et al., 2022 ; De León et al., 2022 ; Zuo, Zhu, & Ling, 2022 ; M. et al., 2005 ; Yin et al., 2022 ; Han & Li, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang & Zhang, 2012 ).…”

“…Multistrain models with vaccination behaviors were studied in ( Rajib Arefin et al., 2019 ; Zuo, Zhu, Meng, et al., 2022 ; De León et al., 2022 ; Zuo, Zhu, & Ling, 2022 ; M. et al., 2005 ; Yin et al., 2022 ; Han & Li, 2022 ; Tchoumi & Tchuenche, 2021 ; Yang & Zhang, 2012 ). Stability analysis of multistrain models was found in ( Allali & Amine, 2022 ; Dong et al., 2017 ; Farah et al., 2021 ; Khatua et al., 2014 ; Khyar & Allali, 2020 ; Meskaf et al., 2020 ; Tchoumi & Tchuenche, 2021 ; Tiwari, Rai, Khajanchi, Gupta, & Misra, 2021 ; Yang & Zhang, 2012 ).…”