Mathematical optimization modeling for estimating the incidence of clinical diseases

Document Type : Research Paper


Department of Mathematics Science, Ministry of Education, Babylon, Iraq


The notion that infectious disease transmission and dissemination are governed by rules that may be expressed mathematically is not new. In fact, the nonlinear dynamics of infectious illness transmission were only fully recognized in the twentieth century. However, with the Coronavirus outbreak, there is a lot of discussion and study regarding the origin of the epidemic and how it spreads before all vulnerable people are infected, as well as ideas about how the disease virulence changes during the epidemic. In this paper, we provide some critical mathematical models which are SIR and SIS and their differences in approach for the interpretation and transmission of viruses and other epidemics as well as formulate the optimal control problem with vaccinations.


[1] H. A. Adamu, M. Muhammad, A. Jingi and M. Usman, Mathematical modelling using improved SIR model with more realistic assumptions, Int. J. Eng. Appl. Sci. 6 (2019) 64–69.
[2] A. Alridha, F.A. Wahbi and M.K. Kadhim, Training analysis of optimization models in machine learning, Int. J. Nonlinear Anal. Appl. 12 (2021) 1453–1461.
[3] R. Anzum and M.Z. Islam, Mathematical modeling of coronavirus reproduction rate with policy and behavioral effects, medRxiv (2021) 1–15.
[4] V. B. Bajiya, S. Bugalia and J.P. Tripathi, Mathematical modeling of COVID-19: impact of non-pharmaceutical interventions in India, Chaos: An Interdisciplinary J. Nonlinear Sci. 30 (2020) 113143.
[5] M. Barro, A. Guiro and D. Ouedraogo, Optimal control of a SIR epidemic model with general incidence function and a time delays, Cubo (Temuco) 20 (2018) 53–66.
[6] M.R. Bhatnagar, COVID-19: Mathematical modeling and predictions, ResearchGate, (2020) 1–7.
[7] P. Bhattacharya, S. Paul and P. Biswas, Mathematical modeling of treatment SIR model with respect to variable contact rate, Int. Proc. Econ. Dev. Res. 83 (2015) 1–8.
[8] B. Cant´o, C. Coll and E. Sanchez, Estimation of parameters in a structured SIR model, Adv. Diff. Equ. 1 (2017) 1–13.
[9] H. H. Dwail and M. A. Shiker, Reducing the time that TRM requires to solve systems of nonlinear equations, IOP Conf. Ser. Mate. Sci. Engin. 2nd Int. Sci. Conf. Al-Ayen University, Thi-Qar, Iraq, 2020, pp: 1–14.
[10] H.S. Husain, An SIR mathematical model for Dipterid disease, J. Phys. Conf. Ser. 2nd Int. Sci. Conf. Al-Ayen University, Thi-Qar, Iraq, 2019, pp: 1–6.
[11] M.J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2011.
[12] A. Kumar and K. Goel, A deterministic time-delayed SIR epidemic model: mathematical modeling and analysis, Theory Biosci. 139 (2020) 67–76.
[13] M.Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases, Springer, 2018.
[14] G.B. Libotte, F.S. Lobato, G.M. Platt and A.J.S. Neto, Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment, Comput. Meth. Prog. Biomed. 196 (2020) 105664.
[15] H.H. Weiss, The SIR model and the foundations of public health, Mate. Math. 3 (2013) 887–1097.
Volume 13, Issue 1
March 2022
Pages 185-195
  • Receive Date: 13 March 2021
  • Revise Date: 29 April 2021
  • Accept Date: 05 May 2021