The SusceptibleβExposedβInfectedβHospitalizedβRemoved (SEIHR) model is a high-utility compartmental framework in mathematical epidemiology that extends the classical SEIR structure by explicitly incorporating hospitalization dynamics. The primary motivation of this model is to support epidemic preparedness and response by forecasting the demand for healthcare resources, particularly hospital beds and intensive care units. Its structure proved especially relevant during large-scale viral outbreaks, where timely anticipation of clinical burden is critical for effective health system management.
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𧱠Compartmental Structure and Flow
The SEIHR model partitions the total population into five epidemiological compartments, each representing a distinct stage of infection and clinical severity.
Susceptible (S)
Individuals who are healthy and vulnerable to infection. They enter the exposed class following effective contact with infectious individuals.
Exposed (E)
Individuals who are infected but in the latent or incubation phase. They are not yet infectious and transition to the infected compartment after incubation.
Infected (I)
Individuals who are infectious and capable of transmitting the disease. This compartment includes both symptomatic and asymptomatic cases.
Hospitalized (H)
Confirmed severe cases requiring medical care or hospitalization. This compartment directly represents healthcare system burden.
Removed (R)
Individuals removed from the transmission process, including both recovered and deceased cases. This compartment aggregates final outcomes.
The flow proceeds from S to E upon exposure, from E to I after incubation, and from I either to H through clinical confirmation or directly to R through recovery without hospitalization. Hospitalized individuals eventually transition to the Removed class.
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π Mathematical Formulation (Ordinary Differential Equation System)
The temporal evolution of the SEIHR model is described by the following system of ordinary differential equations:
dS/dt = β Ξ²β S I
dE/dt = Ξ²β S I β Ο E
dI/dt = Ο E β (Ξ± + Ξ³) I
dH/dt = Ξ± I β Ξ΄ H
dR/dt = Ξ³ I + Ξ΄ H
In this formulation, I represents the total infectious population, encompassing both symptomatic and asymptomatic individuals. Hospitalized individuals are assumed to no longer contribute to transmission.
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π’ Table 1. Parameter Definitions
| Parameter | Definition |
|---|---|
| S | Number of susceptible individuals |
| E | Number of exposed (latent) individuals |
| I | Number of infected and infectious individuals |
| H | Number of hospitalized individuals |
| R | Number of removed individuals (recovered or deceased) |
| Ξ²β | Effective exposure and infection rate |
| Ο | Progression rate from exposed to infected |
| Ξ± | Hospitalization rate of infected individuals |
| Ξ³ | Recovery or removal rate of non-hospitalized infected individuals |
| Ξ΄ | Removal rate of hospitalized individuals |
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π Table 2. Typical Parameter Ranges
| Parameter | Typical Range (per day) | Epidemiological Interpretation |
|---|---|---|
| Ξ²β | 0.15 β 0.35 | Moderate transmission intensity during active outbreaks |
| Ο | 0.10 β 0.20 | Incubation periods of approximately 5β10 days |
| Ξ± | 0.01 β 0.05 | Daily probability of progression to hospitalization |
| Ξ³ | 0.05 β 0.10 | Recovery or removal within 10β20 days |
| Ξ΄ | 0.07 β 0.14 | Average hospitalization duration of 7β14 days |
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π Applicability and Limitations
Primary Application
The SEIHR model is particularly effective for projecting healthcare demand during epidemic outbreaks. By explicitly modeling hospitalization dynamics, it enables estimation of peak hospital occupancy and supports planning for medical resources such as beds, staff, and intensive care capacity.
Model Strength
Incorporation of the exposed compartment allows the model to capture delays between infection and infectiousness, a critical feature for diseases with non-negligible incubation periods.
Granularity Trade-off
The infected compartment aggregates symptomatic and asymptomatic individuals, limiting the ability to separately assess asymptomatic transmission or differential clinical progression.
Outcome Aggregation
The removed compartment combines recovered and deceased individuals, preventing explicit mortality analysis unless further extensions, such as an added death compartment, are introduced.
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π Selected References
Wang, Y. J., Wang, P., Zhang, S. D., et al. Uncertainty modeling of modified SEIR-type epidemic frameworks.
Kong, L., Duan, M., Shi, J., et al. Compartmental structures used in infectious disease modeling.
Eddin, M. S., El Hajj, H., Zayyat, R., and Lee, G. Comparative analysis of compartmental epidemic models.
Newton, E. A. C., and Reiter, P. Mathematical modeling of infectious disease transmission and intervention impact.