Time-dependent solution of the NIMFA equations around the epidemic threshold

Area of Science:

• Epidemiology and Mathematical Modeling
• Computational Biology and Disease Dynamics

Background:

• Most epidemic models utilize non-linear differential equations lacking closed-form solutions.
• This absence limits precise understanding of viral dynamics and disease progression.
• Accurate modeling is crucial for predicting and controlling infectious disease outbreaks.

Purpose of the Study:

• To develop a method for solving differential equations in epidemic models.
• To analyze the susceptible-infected-susceptible (SIS) epidemic process with heterogeneous parameters.
• To provide accurate solutions for epidemic dynamics, particularly around the epidemic threshold.

Main Methods:

• Employed the N-intertwined mean-field approximation for the SIS epidemic process.
• Solved differential equations for heterogeneous spreading parameters on arbitrary contact networks.
• Focused on initial viral states that are small or parallel to the steady-state vector.

Main Results:

• Successfully solved the differential equations under specific initial conditions.
• Numerical simulations confirmed the accuracy of the solution around the epidemic threshold.
• The method also demonstrated accuracy above the threshold and for general initial states below steady-state.

Conclusions:

• The developed method provides accurate solutions for complex epidemic models.
• This approach enhances the understanding of viral dynamics, overcoming limitations of non-closed-form solutions.
• The findings are applicable to various contact networks and initial conditions, aiding epidemic control strategies.