Dynamics of a Fractional-Order Hepatitis B Epidemic Model and Its Solutions by Nonstandard Numerical Schemes

Dynamics and numerical approximations for a fractional-order SIS epidemic model with saturating contact rate

“…In Examples 1-3, we have seen the differences between the numerical approximations generated by the NSFD schemes and the standard schemes. Note that these differences have been showed in the previous works on NSFD schemes for ODEs, PDEs, and FDEs (see, for example, Adekanye and Washington 2018;Arenas et al 2016;Hoang and Nagy 2019;Hoang and Egbelowo 2020;Mickens 1993Mickens , 2000Mickens , 2002Mickens , 2005. The I -component generated by the NSFD scheme with t = 2.0 after 80 iterative steps…”

“…Therefore, fractional-order models can provide better observations on transmission mechanism of viruses in infectious diseases. Recently, a fractional-order logistic model with feedback control and a fractional-order hepatitis B model have been formulated and analyzed (Hoang and Nagy 2019;Hoang and Egbelowo 2020). However, to the best of our knowledge, the fractional-order version of the model (1) has not been studied.…”

“…Nowadays, NSFD methods have become one of the most effective and powerful approaches to solve ODEs, PDEs, and FDEs (see, for example, Adekanye and Washington 2018;Arenas et al 2016;Cresson and Pierret 2016;Mickens 1993Mickens , 2000Mickens , 2002Mickens , 2005Sweilam et al 2019;Temimi and Ben-Romdhane 2016;Wood and Kojouharov 2015;Wood et al 2017;Yang et al 2016 and references therein). Recently, NSFD schemes for some ODEs and FDEs arising in applied fields have been constructed and analyzed (Dang and Hoang 2016, 2019a, b, 2020aHoang and Nagy 2019;Hoang and Egbelowo 2020). However, to the best of our knowledge, NSFD schemes for FDEs in general are few and NSFD schemes for the model (2) in particular have not been studied.…”

Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

“…For the discrete derivatives given in system (33), we have many options for the denominator function ϕ. We have chosen ϕ(h) = (1 − exp(−hp))/p, where p = max A, ∆, µ 0 , δ I , δ I E are parameters of the model and included in the numerical scheme (33). This particular ϕ usually provides better numerical results based on previous articles related to NSFD schemes [113,114].…”

“…Numerous mathematical models represented by means of a system of differential equations, with or without delay, have been discretized by means of the non-standard finite difference method proposed by Ronald Mickens, see [24][25][26][27][28][29][30][31][32][33][34]. Their use is mainly because they are very effective in preserving certain qualitative properties of the original differential equations and the convergence, consistency and stability of their solutions have been demonstrated, see [35][36][37][38][39][40][41][42][43][44][45][46].…”