**6. Conclusions**

We developed a new strategy to design an interval state estimator for a fourth-order nonlinear discrete-time SEIR epidemic model subject to uncertain input, disturbances and measurement noise. The proposed method only requires the bounded values instead of exact values for state disturbance, unknown input, and parameters. In addition, no bounds on the time-varying transmission rate (susceptible to the infected stage) are required. The MST is widely used to design such an observer, but obtaining a non-negative model is not always feasible. Therefore, the proposed interval state estimator relaxes such restrictions by estimating the four compartment states using the observability matrix instead of point-wise estimation. The finite-time convergence of the interval width for the proposed approach is investigated to demonstrate its stability and performance. In addition, the interval widths' upper bound is estimated a priori. Finally, two numerical simulations are conducted to test the performance of the designed method. It is concluded that the proposed interval estimator generates more accurate boundaries and performs better. However, the proposed technique can currently be applied in linear and nonlinear discrete-time models. The interval estimator design approach for continuous-time systems will be investigated in the future.

**Author Contributions:** Conceptualization, A.K.; methodology, A.K.; software, A.K.; validation, A.K., X.B.; formal analysis, A.K., B.Z.; investigation, A.K., B.Z., P.Y.; writing—original draft preparation, A.K., X.B. and M.I.; writing—review and editing, A.K., A.R. and W.X.; supervision, B.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the National Natural Science Foundation of China (NSFC) under the grant 62173234 and 62003217.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
