Nikhil Chanauria, Syed Abbas
Abstract:
Classical infectious disease models often neglect the interplay of spatial diffusion,
infection-age structure, and time-dependent controls. We address this gap by analyzing
a spatiotemporal SIQRV reaction-diffusion model structured by infection age,
incorporating vaccination, quarantine, and waning immunity.
The simultaneous inclusion of nonlocal infection-age structure, spatial diffusion,
and time-dependent controls introduces major analytical challenges,
including coupled transport-diffusion dynamics, nonlinear nonlocal incidence,
and the derivation of optimality conditions in infinite-dimensional spaces.
Using semigroup theory and spectral methods, we establish well-posedness,
derive the basic reproduction number \(\mathcal{R}_0\), and analyze equilibrium stability.
An optimal control framework is introduced with vaccination, social distancing,
and quarantine as time-varying interventions. Necessary conditions are derived via
an adjoint system and solved using a forward-backward sweep method.
Simulations with measles-like parameters show that spatially targeted,
age-structured interventions effectively suppress outbreaks and improve resource
allocation. This study underscores the importance of integrating spatial and
temporal heterogeneities in epidemic control strategies.
Submitted May 5, 2026. Published June 29, 2026.
Math Subject Classifications: 5F50, 35K57, 92D30.
Key Words: Infection-age structured; reaction-diffusion; stability analysis;
optimal control.
DOI: 10.58997/ejde.2026.45
Show me the PDF file (1023 KB), TEX file for this article.
 |
Nikhil Chanauria School of Mathematical and Statistical Sciences Indian Institute of Technology Mandi Mandi, H.P., 175005, India email: kumar.nikhil437@gmail.com |
|---|---|
 |
Syed Abbas School of Mathematical and Statistical Sciences Indian Institute of Technology Mandi Mandi, H.P., 175005, India email: abbas@iitmandi.ac.in, sabbas.iitk@gmail.com |
Return to the EJDE web page