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Predicting The Correct Infection Function Of An Epidemic Model

Predicting infection function of epidemic model is essential in studying infectious diseases. The conventional differential equation model of infectious illness is based on known disease features and has long been investigated and predicted epidemic dynamics. Nonlinear infection functions are used in the majority of epidemic models. Nonlinearity, on the other hand, emerges swiftly from the numerous illness and vulnerability term combinations. To deal with nonlinearity's challenges, researchers typically employ the bifurcation theory of nonlinear equations to produce estimates, which they then refine using expert knowledge.

Despite advances in nonlinear epidemic model analysis, determining the optimal infection function remains technically infeasible. The functions are related to the number of vulnerable and infected people and include environmental and behavioural variables. The Holling type function is mathematically applied to the infection function to account for such behaviour. Any mistake in selecting the infection function directly impacts the precision of model prediction. However, depending on existing data is insufficient; technical expertise of the environment, human behaviour, and virus strain features are also required. As a result, improved procedures are needed.

Machine learning and similar neural-network models have substantially improved the predictability of nonlinear functions in the modern industry. A neural network is built layer by layer after the neuromorphology of the human brain, with input layers, output layers, neurons, and activation functions (synapses) at each layer. Most research has been on linear hybrid models, with only a few studies focusing on nonlinear issues. A team of researchers led by Chentong Li and Changsheng Zhou from Guangdong Academy of Science and Guangzhou University in China studied the power of a hybrid nonlinear epidemic neural network in predicting the correct infection function of an epidemic model. To assure model trainability, they integrated the bifurcation theory of the nonlinear differential model with the mean-squared error loss and designed a unique loss function. They used a model using accurate COVID-19 data to determine the changing law of its infectivity.

Hybrid Epidemic Model

They employed six requirements (the fundamental features fulfilled by most epidemic models) to forecast the correct infection function based on the unique circumstances of ordinary differential equations and the basic properties of epidemic models. The Euler and Runge–Kutta techniques are the most successful and extensively utilised for solving ordinary differential equations. The Runge–Kutta technique, which stems from the integral form of the ordinary differential equation, is used to compute the numerical solution at each time point. The Euler approach is less precise and stems from the discrete form of differentiation. 's work, Introduction to the Basic Properties of an Epidemic Model and the Forward Bifurcation of an Epidemic System, explained the vanishing gradient requirements that result in the hybrid model's untrainability. They trained a hybrid model using produced data using the typical fixed-step numerical approach, and the numerical results confirm its accuracy.

Model Application To COVID-19 Real Data

Using U.S. COVID-19 actual data of two phases from June 16 to October 31, 2021, and December 12, 2021, to February 11, 2022, the researchers used the fitted models to forecast ground-truth changes in historical COVID-19 infectivity. The significant strains during COVID-19 transmission were delta and omicron, as indicated by the two peaks. During the first period, infectivity dropped and then stabilized. In the second phase, infectivity rose at first and then remained steady. However, when the fitted results of the two infection functions are compared.

The study revealed that the infection function changed faster in the second period than it did in the first. Similarly, the infection rate was more significant in the second period than the first. The drop in the first period might be attributed to an increase in vaccinated persons. In contrast, the growth in the second period may be attributed to the introduction of the omicron strain and a fall in temperature. It was proved through this practical application example that the technique could comprehend otherwise concealed information in restricted real-world data, which not only broadens application breadth but also considerably boosts model flexibility. The suggested technique provides computational support and a theoretical foundation for future research on infectious illnesses.


The trials demonstrated that the model could match the data quite well. The study supplied the parameters required to complete the problems and a specific implementation approach and its published computer code, which may be utilised in similar hybrid-model applications. The researchers reported the method's application using genuine COVID-19 data from the United States. The findings demonstrated that the suggested model identifies the hidden information behind restricted accurate data, increasing its relevance to infectious disease models. This paper sheds fresh light on the capabilities of hybrid neural networks in dealing with nonlinear situations using nonlinear ordinary differential equations.

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