Applications of artificial neural network to solve the nonlinear COVID-19 mathematical model based on the dynamics of SIQ

Figures & data

Table 1. Comprehensive details of each parameter of the nonlinear SIQ system.

Parameters	Description
$\alpha$	Half saturation constant
$a$	Recruitment rate
$\eta$	Positive value
$\mu$	Natural death rate
$\beta$	Transmission infection rate
M	Migrants number
${\delta }_1$	Recovery rate of infective population
$\theta$	Infected migrants’ rate
K	Contact tracing rate
${\delta }_2$	Recovery rate of quarantined population
$\sigma$	0.59 per day
${\alpha }_1$	Disease-associated infective population’s death rate
${\alpha }_2$	Disease-associated quarantine’s population death rate
y1, y2 and y3	Contents for the initial conditions (ICs)

Figure 1. Workflow structure of the proposed stochastic structure for the SIQ dynamical model of COVID-19.

Figure 2. Proposed framework based on the single neuron.

Figure 3. Stochastic structure for the SIQ dynamical COVID-19 model.

Figure 4. MSE and state transitions for the SIQ dynamical COVID-19 model. (a) Case 1: MSE, (b) Case 2: MSE, (c) Case 3: MSE, (d) Case 1: Values of the state transition, (e) Case 2: Values of the state transition, (f) Values of the state transition.

Figure 5. Comparison and EHs values using the ANNs-LMB to solve the SIQ dynamical system based COVID-19. (a) Case 1: Comparison, (b) Case 2: Comparison, (c) Case 3: Comparison, (d) Case 1: EHs, (e) Case 2: EHs, (f) Case 3: EHs.

Figure 6. Regression measures through the ANNs-LMB for case 1.

Figure 7. Regression measures through the ANNs-LMB for case 2.

Figure 8. Regression measures through the ANNs-LMB for case 3.

Table 2. Proposed ANNs-LMB for the SIQ dynamical COVID-19 model.

	MSE
Case	[Training]	[Verification]	[Testing]	Performance	Gradient	Mu	Epoch	Time
I	2.708 × 10^−05	4.002 × 10^−05	2.811 × 10^−05	2.71 × 10^−05	2.89	1.00 × 10^−02	1000	6
2	2.825× 10^−07	3.454 × 10^−07	2.612 × 10^−07	2.83 × 10^−07	1.87	1.00 × 10^−04	1000	4
3	2.932 × 10^−06	1.449 × 10^−05	1.392 × 10^−15	2.93 × 10^−06	2.95	1.00 × 10^−03	1000	4

Figure 9. Results comparisons to solve each case of the nonlinear dynamical SIQ-based COVID-19 model. (a) Results for case 1, (b) Results for case 2, (c) Results for case 3.

Figure 10. AE for each case of the nonlinear dynamical SIQ-based COVID-19 model, (a) AE: case 1, (b) AE: case 2, (c) AE: case 3.

Data availability statement

All data generated or analyzed during this study are included in this article.