Numerical study of a two-dimensional eco-epidemiological model with diffusion and convex incidence rate: Unconditionally positivity preserving method

[1] N. Ahmed, S.S. Tahira, M. Rafiq, M.A. Rehman, M. Ali, M.O. Ahmad, Positivity preserving oper-
ator splitting nonstandard finite difference methods for SEIR reaction diffusion model, Open Math.
17 (2019) 313–330.
[2] N. Ahmed, Z. Wei, D. Baleanu, M. Rafiq, M.A. Rehman, Spatio-temporal numerical modeling of
reaction-diffusion measles epidemic system, Chaos 29 (2019) 103101.
[3] F. Al-Showaikh, Numerical modelling of some systems in the biomedical sciences, Ph.D. thesis,
Brunel University, School of Information Systems, Computing and Mathematics, 1998.
[4] J.A. Aledo, C. Andreu-Vilarroig, J.-C. Cortes, J.C. Orengo, R.-J. Villanueva, On the epidemiologi-
cal evolution of colistin-resistant acinetobacter baumannii in the city of valencia: An agent-based
modelling approach, Math. Model. Nat. Phenom. 18 (2023) 33.
[5] S. Bagheri, M.H. Akrami, G.B. Loghmani, M. Heydari, Traveling wave in an eco-epidemiological
model with diffusion and convex incidence rate: Dynamics and numerical simulation, Math. Com-
put. Simul. 216 (2024) 347–366.
[6] A.M. Bate, F.M. Hilker, Preytaxis and travelling waves in an eco-epidemiological model, Bull.
Math. Biol. 81 (2019) 995–1030.
[7] B. Buonomo, D. Lacitignola, On the dynamics of an seir epidemic model with a convex incidence
rate, Ric. Mat. 57 (2008) 261–281.
[8] B. Buonomo, S. Rionero, On the lyapunov stability for SIRS epidemic models with general nonlin-
ear incidence rate, Appl. Math. Comput. 217 (2010) 4010–4016.
[9] Y. Cai, Y. Kang, W. Wang, A stochastic SIRS epidemic model with nonlinear incidence rate, Appl.
Math. Comput. 305 (2017) 221–240.
[10] B.M. Chen-Charpentier, H.V. Kojouharov, An unconditionally positivity preserving scheme for
advection-diffusion reaction equations, Math. Comput. Model 57 (2013) 2177–2185.
[11] C. Cosner, D.L. DeAngelis, J.S. Ault, D.B. Olson, Effects of spatial grouping on the functional
response of predators, Theor. Popul. Biol. 56 (1999) 65–75.
[12] K. Dariva, T. Lepoutre, Influence of the age structure on the stability in a tumor-immune model for
chronic myeloid leukemia, Math. Model. Nat. Phenom. 19 (2024) 1.
[13] R.U. Din, E.A. Algehyne, Mathematical analysis of COVID-19 by using SIR model with convex
incidence rate, Results Phys. 23 (2021) 103970.
[14] P. Dutta, D. Sahoo, S. Mondal, G. Samanta, Dynamical complexity of a delay-induced eco-epidemic
model with Beddington–DeAngelis incidence rate, Math. Comput. Simul. 197 (2022) 45–90.
[15] D. Greenhalgh, Q.J. Khan, F.A. Al-Kharousi, Eco-epidemiological model with fatal disease in the
prey, Nonlinear Anal. Real World Appl. 53 (2020) 103072.

[16] E.E. Holmes, M.A. Lewis, J.E. Banks, R.R. Veit, Partial differential equations in ecology: spatial
interactions and population dynamics, Ecology 75 (1994) 17–29.
[17] F. Izadi, Using nonstandard finite difference methods for solving converted schrodinger equation to
an ODE, Iran. J. Optim. 13 (2021) 13–27.
[18] Y. Jin, W. Wang, S. Xiao, An SIRS model with a nonlinear incidence rate, Chaos Solit. Fract. 34
(2007) 1482–1497.
[19] A. Khan, R. Zarin, G. Hussain, N.A. Ahmad, M.H. Mohd, A. Yusuf, Stability analysis and optimal
control of covid-19 with convex incidence rate in khyber pakhtunkhawa (pakistan), Results Phys.
20 (2021) 103703.
[20] A. Khan, R. Zarin, G. Hussain, A.H. Usman, U.W. Humphries, J.G. Aguilar, Modeling and sensi-
tivity analysis of HBV epidemic model with convex incidence rate, Results Phys. 22 (2021) 103836.
[21] A. Korobeinikov, P.K. Maini. Non-linear incidence and stability of infectious disease models, Math.
Med. Biol. 22 (2005) 113–128.
[22] G.-H. Li, Y.-X. Zhang, Dynamic behaviors of a modified SIR model in epidemic diseases using
nonlinear incidence and recovery rates, Plos One. 12 (2017) 0175789.
[23] L. Liu, D.P. Clemence, R.E. Mickens, A nonstandard finite difference scheme for contaminant
transport with kinetic langmuir sorption, Numer. Methods Partial Differ. Equ. 27 (2011) 767–785.
[24] R.E. Mickens, A best finite-difference scheme for the fisher equation, Numer. Methods Partial Dif-
fer. Equ. 10 (1994) 581–585.
[25] R.E. Mickens, Exact solutions to a finite-difference model of a nonlinear reaction-advection equa-
tion: Implications for numerical analysis, Numer. Methods Partial Differ. Equ. 5 (1989) 313–325.
[26] A. Mondal, A.K. Pal, G.P. Samanta, Analysis of a delayed eco-epidemiological pest–plant model
with infected pest, Biophys Rev. Lett. 14 (2019) 141–170.
[27] A. Mondal, A. Pal, G. Samanta, On the dynamics of evolutionary leslie-gower predator-prey eco-
epidemiological model with disease in predator, Ecol. Genet. Genom. 10 (2019) 100034.
[28] J.D. Murray, Mathematical Biology: II: Spatial Models and Biomedical Applications, volume 3.
Springer, 2003.
[29] A. Nauman, M. Rafiq, M.A. Rehman, M. Ali, M.O. Ahmad, Numerical modeling of seir measles
dynamics with diffusion, Commun. Math. Appl. 9 (2018) 315.
[30] A. Pal, A. Bhattacharyya, A. Mondal, Qualitative analysis and control of predator switching on
an eco-epidemiological model with prey refuge and harvesting, Results Control Optim. 7 (2022)
100099.
[31] A.K. Pal, A. Bhattacharyya, A. Mondal, S. Pal, Qualitative analysis of an eco-epidemiological
model with a role of prey and predator harvesting, Z. Naturforsch. A. 77 (2022) 629–645.

[32] A. Pal, G. Samanta, Stability analysis of an eco-epidemiological model incorporating a prey refuge,
Nonlinear Anal. Model. Control 15 (2010) 473–491.
[33] M.S. Rahman, S. Chakravarty, A predator-prey model with disease in prey, Nonlinear Anal. Model.
Control 18 (2013) 191–209.
[34] G.U. Rahman, K. Shah, F. Haq, N. Ahmad, Host vector dynamics of pine wilt disease model with
convex incidence rate, Chaos Solit. Fract. 113 (2018) 31–39.
[35] L.-I.W. Roeger, Dynamically consistent discrete-time SI and SIS epidemic models, Conf. Publ. 2013
(2013) 653–662.
[36] S. Saha, A. Maiti, G.P. Samanta, A Michaelis–Menten predator–prey model with strong Allee effect
and disease in prey incorporating prey refuge, Int. J. Bifurc. Chaos 28 (2018) 1850073.
[37] S. Saha, G.P. Samanta, A prey-predator system with disease in prey and cooperative hunting strat-
egy in predator, J. Phys. A: Math. Theor. 53 (2020) 485601.
[38] G. Samanta, Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species,
Forum for Interdisciplinary Mathematics. Springer Singapore, 2021.
[39] X.-F. San, Z.-C. Wang, Z. Feng, Spreading speed and traveling waves for an epidemic model in a
periodic patchy environment, Commun. Nonlinear Sci. Numer. Simul. 90 (2020) 10538.
[40] N. Santra, S. Saha, G. Samanta, Exploring cooperative hunting dynamics and prcc analysis: in-
sights J. Phys. A: Math. Theor. 57 (2024) 305601.
[41] N. Sapoukhina, Y. Tyutyunov, R. Arditi, The role of prey taxis in biological control: a spatial
theoretical model, Am. Nat. 162 (2003) 61–76.
[42] M. Sieber, H. Malchow, F.M. Hilker, Disease-induced modification of prey competition in eco-
epidemiological models, Ecol. Complex. 18 (2014) 74–82.
[43] G.D. Smith, Numerical solution of partial differential equations: finite difference methods, Oxford
University Press, 1985.
[44] H. Yang, Y. Wang, S. Kundu, Z. Song, Z. Zhang, Dynamics of an SIR epidemic model incorporating
time delay and convex incidence rate, Results Phys. 32 (2022) 105025.