[1] Baccella, G.,1995. semi-artinian V-rings and semi-artinian von Neumann regular rings, J. Algebra 173, pp 587-612.
[2] Elliott, G A., 1976. On the Classification of Inductive Limits of Sequences of Semisimple FiniteDimensional Algebras J. Algebra, 38, pp 29-44.
[3] K.R.Goodearl, 1979. Von Neumann Regular Rings, Pitman, London.
[4] Gooderl, K.R., 1980. Artinian and Noetherian modules over regular rings. Comm. Algebra, 8(5), pp.
477-504. doi:10.1080/00927878008822470.
[5] Goursaud, J.M. and Jeremy. L. 1977. Une notion de rang dans les facteurs reguliers autoinjectifs a
droite, Comm. Alg. 5 , pp 829–839.
[6] Fisher, JW. and Snider, R., 1974. Prime von Neumann regular rings and primitive group rings.
Proc.Amer.Math.Soc, 44, (2) doi:10.2307/2040414
[7] Herbera, D., 2009. Simple modules over small rings, Modules and representations, Contemp.
Math.,480, Amer. Math. Soc., Providence, RI, pp 189-205.
[8] Momtahan, E., 2011. On Semi-Artinian weakly co-emisimple modules, Bultein of IMS,(37), 3, pp 149-157.
[9] Osofsky, B., 1966, cyclic injective modules of full linear rings, Proc. Amer. Math. Soc., 17, pp 247-252.
[10] Wisbuer, R., 1991. Foundations of Rings and Module Theory, Gordon and Breach
[14] Kannenberg, J., Trawinski, H., Henschler, R., Buhmann, R., Hönemann, M. and Jassoy, C.,
2022. Antibody course and memory B-cell response in the first year after severe acute respiratory syndrome coronavirus 2 infection. The Journal of Infectious Diseases, 226(4), pp. 664–672.
doi.org/10.1093/infdis/jiac034
[15] Gazit, S., Shlezinger, R., Perez, G., Lotan, R., Peretz, A., Ben-Tov, A., Herzel, E., Alapi, H., Cohen, D., Muhsen, K. and Chodick, G., 2022. SARS-CoV-2 naturally acquired immunity vs. vaccineinduced immunity, reinfections versus breakthrough infections: a retrospective cohort study. Clinical
Infectious Diseases, 75(1), pp. 545–551. DOI:10.1093/cid/ciac262
[16] Vo, A.D., La, J., Wu, J. T., Strymish, J. M., Ronan, M., Brophy, M., Do, N. V., Branch-Elliman,
W., Fillmore, N. and Monach, P. A., 2022. Factors Associated with Severe Covid-19 Despite Vaccination: A Nationwide, Retrospective Cohort Study. Research Square, 2022. doi.org/10.21203/rs.3.rs1654435/v1
[17] Althoff, A., Papasavas, P., Olugbile, S., Wu, U., Roberts, A. L., O’Sullivan, D. M., McLaughlin, T.,
Mather, J. F., Steinberg, A. C., Orlando, R. and Kumar, A., 2022. Factors affecting seroreversion by
6 months among healthcare workers in Connecticut. The Journal of Hospital Infection, 121, pp. 132.
doi.org/10.1016/j.jhin.2021.12.001
[18] Sumi, T. and Harada, K., 2022. Immune response to SARS-CoV-2 in severe disease and long COVID19. Iscience, 25 (8), pp. 104723. doi.org/10.1016/j.isci.2022.104723
[19] Tegeler, C.M., Bilich, T., Maringer, Y., Salih, H. R., Walz, J. S., Nelde, A. and Heitmann, J. S., 2022.
Prevalence of COVID-19-associated symptoms during acute infection in relation to SARS-CoV-2-
directed humoral and cellular immune responses in a mild-diseased convalescent cohort. International
Journal of Infectious Diseases, 120 , pp.187–195. doi.org/10.1016/j.ijid.2022.04.019
[20] Yao, L., Lu, L. and Ma, W., 2022. Immunopathological changes, complications, sequelae and immunological memory in COVID-19 patients. Heliyon, 8 (4), pp. 1–13.
doi.org/10.1016/j.heliyon.2022.e09302
[21] Djilali, S., Ghanbari, B., 2020. Coronavirus pandemic: A predictive analysis of the peak outbreak
epidemic in South Africa, Turkey, and Brazil. Chaos, Solitons and Fractals, 138 , pp. 109971.
doi.org/10.1016/j.chaos.2020.109971
[22] Liu, Y., Yan, LM., Wan, L., Xiang, TX., Le, A., Liu, JM., Peiris, M., Poon, LL., Zhang, W., 2020.
Viral dynamics in mild and severe cases of COVID-19. The Lancet infectious diseases, 20 (6), pp.
656–657. doi.org/10.1016/ S1473-3099(20)30231-0
[23] Kassa, S. M., Njagarah, J. B. H. and Terefe, Y. A., 2020. Analysis of the mitigation strategies
for COVID-19: From mathematical modelling perspective. Chaos, Solitons and Fractals, 138,
pp.109968. doi.org/10.1016/j.chaos.2020.109968
[24] Mohammadaliee, B, Roomi, V., Samei, M. E., 2024. SEIARS model for analyzing COVID‑19 pandemic process via Ψ−Caputo fractional derivative and numerical simulation. Scientific Reports, 2024,
14:723. https://doi.org/10.1038/s41598-024-51415-x
[25] Mohammadaliee, B, Roomi, V., Samei, M. E., Rezapour, S., 2025. Optimal control strategies
and cost-effectiveness analysis for infectious diseases under fractal-fractional derivative: a case
study of Cholera outbreak. Journal of Applied Mathematics and Computing, 71, pp. 4197-4226.
https://doi.org/10.1007/s12190-024-02331-w
[26] Janatolmakan, F., Roomi, V., Gharahasanlou, T. K., 2024. Stability and Numerical Simulation of an
SCIRS Epidemic Model for Covid-19 Transmission by Caputo Derivative of Fractional Order. Journal
of Mathematical Extension, 18(11), pp. 1-35. http://10.0.119.31/JME.2024.3221
[27] Kilbas, A.A., Srivastava, H. M. and Trujillo, J.J., 2006. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204.
[28] Van den Driessche, P., Watmough, J., 2002. eproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180(1-2), pp.
29–48. doi.org/10.1016/S0025-5564(02)00108-6
[29] Hassard, B. D., Kazarinoff, N. D., Wan, Y. H., 1981. Theory and Applications of Hopf Bifurcation.
Cambridge University Press 41.
[30] Podlubny, I, 1999. Fractional Differential Equations. Academic Press, San Diego, Series in Mathematics in Science and Engineering, 198.
[31] Podlubny, I, 1999. Fractional Differential Equations: An Introduction to Fractional Derivatives,
Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, 198.
[32] Powell, D. R. Fair, J. LeClaire, R. J. Moore, L. M. and Thompson, D., 2005. Sensitivity analysis of
an infectious disease model. Proceedings of the International System Dynamics Conference.