the model is then called the SEIR model. Figure 1.6 shows data representation at different point of contact.
Figure 1.7 is about SIR model. The model consists of three comparments:
Figure 1.6 Exposed, infection and recovery transmission in SEIR model. (a) Any susceptible can be exposed by rate of per contact point. (b) Infection occurs at rate per contact and (c) recovery occurs at rate for infected population.
Figure 1.7 SIR model.
S: The number of susceptible individuals. When a susceptible and an infectious individual come into “infectious contact”, the susceptible individual contracts the disease and transitions to the infectious compartment.
I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.
R: The number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called “recovered” or “resistant”.
1.3.2 SIR Model (Susceptible-Infected-Recovered)
The outbreak prediction has become highly complicated for emerging scientific science due to the pandemic scenario of COVID-19 disease cases around the world. To accurately forecast the forecasts, many epidemiological mathematical models of spread are growing daily. In this analysis, to analysis the various parameters of this model for India, the classical susceptible-infected-recovered (SIR) modelling method was used. By considering various governmental lockdown initiatives in India, this method was studied [14].
Estimation of parameters of SIR model of India using an actual data set:
Fundamental models based on compartments, as seen in the following, were used for the epidemic mathematical model:
1 (Susceptible->Infectible) SI model,
2 (Susceptible->Infectible-> Susceptible) SIS model, and
3 (Susceptible->Infectible-> Recovery/Removed) SIR model.
The standard SIR model is basically a series of differential equations that can be classified as susceptible (if previously unexposed to pandemic disease), infected (if presently conquered by pandemic disease), and removed (either by death or recovery) [15].
1.4 Conclusion
The goal of this chapter was to present some of the machine learning and AI principles and methodologies and explore some of their possible applications in different aspects of computational mechanics. The methodologies outlined herein are maturing rapidly, and many new applications are likely to be found in computational mechanics. Undoubtedly, AI methodologies would inevitably become, to the same degree as today’s “traditional” algorithmic devices, a natural and indispensable part of the set of computer-based engineering resources. These instruments would then greatly elevate the role of computers in engineering from the current focus on calculation to the much wider field of reasoning.
References
1. Min Cai, Huan-Shui Zhang and Wei Wang, “A power control algorithm based on SIR with multiplicative stochastic noise,” Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826), Shanghai, China, 2004, pp. 2743-2746 vol. 5, doi: 10.1109/ICMLC.2004.1378324.
2. M. Muselli, A. Bertoni, M. Frasca, A. Beghini, F. Ruffino and G. Valentini, “A Mathematical Model for the Validation of Gene Selection Methods,” in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 5, pp. 1385-1392, Sept.-Oct. 2011, doi: 10.1109/TCBB.2010.83.
3. Dutta, Nabanita & Subramaniam, Umashankar & Sanjeevikumar, P.. (2018). Mathematical models of classification algorithm of Machine learning. 10.5339/qproc.2019.imat3e2018.3.
4. KNN Model-Based Approach in Classification, Gongde Guo1, Hui Wang 1, David Bell 2, Yaxin Bi 2, and Kieran Greer 1, School of Computing and Mathematics, University of Ulster, Newtownabbey, BT37 0QB, Northern Ireland, UK.
5. S. Ji, L. T. Watson and L. Carin, “Semi supervised Learning of Hidden Markov Models via a Homotopy Method,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 2, pp. 275-287, Feb. 2009, doi: 10.1109/TPAMI.2008.71.
6. Pavithra, M., Rajmohan, R., Kumar, T. A., & Ramya, R. (2021). Prediction and Classification of Breast Cancer Using Discriminative Learning Models and Techniques. Machine Vision Inspection Systems, Volume 2: Machine Learning-Based Approaches, 241-262.
7. SanghamitraMohanty, HimadriNandini Das Bebartta, “Performance Comparison of SVM and K-NN for Oriya Character Recognition”, (IJACSA) International Journal of Advanced Computer Science and Applications, Special Issue on Image Processing and Analysis, 2011, pp. 112-115
8. D. Bouchoffra and F. Ykhlef, “Mathematical models for machine learning and pattern recognition,” 2013 8th International Workshop on Systems, Signal Processing and their Applications (WoSSPA), Algiers, 2013, pp. 27-30, doi: 10.1109/WoSSPA.2013.6602331.
9. R. Veena, S. Fauziah, S. Mathew, I. Petra and J. Hazra, “Data driven models for understanding the wind farm wake propagation pattern,” 2016 International Conference on Cogeneration, Small Power Plants and District Energy (ICUE), Bangkok, 2016, pp. 1-5, doi: 10.1109/COGEN.2016.7728969.
10. H. J. Vishnukumar, B. Butting, C. Müller and E. Sax, “Machine learning and deep neural network — Artificial intelligence core for lab and real-world test and validation for ADAS and autonomous vehicles: AI for efficient and quality test and validation,” 2017 Intelligent Systems Conference (IntelliSys), London, 2017, pp. 714-721, doi: 10.1109/IntelliSys.2017.8324372.
11. A. Salaün, Y. Petetin and F. Desbouvries, “Comparing the Modeling Powers of RNN and HMM,” 2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA), Boca Raton, FL, USA, 2019, pp. 1496-1499, doi: 10.1109/ICMLA.2019.00246.
12. S. A. Selvi, T. A. kumar, R. S. Rajesh and M. A. T. Ajisha, “An Efficient Communication Scheme for Wi-Li-Fi Network Framework,” 2019 Third International conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC), Palladam, India, 2019, pp. 697-701, doi: 10.1109/I-S MAC47947.2019.9032650.
13. Mathematical models and deep learning for predicting the number of individuals reported to be infected with SARS-CoV-2‵ A. S. Fokas, N. Dikaios and G. A. Kastis.
14. M. A. Bahloul, A. Chahid and T. -M. Laleg-Kirati, “Fractional-Order SEIQRDP Model for Simulating the Dynamics of COVID-19 Epidemic,” in IEEE
