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Compartmental models, applied to investigate the dynamics of infectious diseases such as COVID-19, swine influenza, tuberculosis, measles, and strep throat, also determine evaluating the risk factors, suitable treatment methods, and predicting and controlling a possible outbreak.

Mathematical modeling of infectious diseases with the SIR (susceptible-infected-recovered) framework was inititated by Bernoulli in [6]. Motivated by our earlier and current research on mathematical modeling of HIV-1 in [1], Mammary Tumors and Pseudomonas putida in [2], swine influenza in [4], and tuberculosis in [5], we observe that time-scale modeling approach play an important role to recover information from experimental data with varying domains (time-scales), [7] and [8]. In this talk, we propose time-scale models, covering wide classes of models from continuous to discrete, for infectious diseases, especially HIV, swine influenza, and tuberculosis. In addition, we discuss the stability results of the models based on the basicreproduction number and demonstrate our numerical results.

REFERENCES

[1]. Akın, E., Yeni, G., and Perelson, A.S., Continuous and Discrete Modeling of HIV-1 Decline on Therapy, J. Math. Bio., https://doi.org/10.1007/s00285-020-01492-z , 2020.

[2]. Akın, E., Pelen, N.N., Tiryaki, I.U, and Yalcin, F., Parameter identification for gompertz and logistic dynamic equations, Plos One, https://doi.org/10.1371/journal.pone.0230582, 2020.

[3]. Akın, E. and Yeni, G. On Exact Solutions to Epidemic Dynamic Models, J. Appl. Anal. Comp. 10(6), 2020, 2299-2312.

[4]. Akın, E., Yeni, G., and Vaidya, N., Time Scale Theory on Stability of Explicit and Implicit Discrete Epidemic Models: Applications to Swine Flu Outbreak, J. Math. Bio. Accepted, 2023.

[5] Akın, E., Yeni, G., Konur, D., Isik, R.S., and Isik, M.R. Global Dynamics of Tuberculosis Transmission by Continuous and Discrete SEIR Models. Submitted, 2023.

[6] Bernoulli, D., Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir. Histoire de l'Acad., Roy. Sci.(Paris) avec Mem, 1760, 1-45.

[7]. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales, An Introduction with Applications, Birkhaeuser, Boston, 2001.

[8]. Bohner, M. and Peterson, A., Advances in Dynamic Equations on Time Scales, Birkhaeuser, Boston, 2003.