Spatial heterogeneity and nonlinear transmission drive tuberculosis hotspots: a reaction–diffusion modeling study

Olumuyiwa James Peter; Azhar Iqbal Kashif Butt; Sharifah Sakinah Syed Ahmad; Fatemah H. H. Al Mukahal; Olumuyiwa James Peter; Azhar Iqbal Kashif Butt; Sharifah Sakinah Syed Ahmad; Fatemah H. H. Al Mukahal

doi:10.3934/math.2026788

AIMS Mathematics

2026, Volume 11, Issue 7: 19400-19439. doi: 10.3934/math.2026788

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Spatial heterogeneity and nonlinear transmission drive tuberculosis hotspots: a reaction–diffusion modeling study

1.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai, Tamil Nadu, India
2.
Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo, Ondo State, Nigeria
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
4.
Faculty of Artificial Intelligence and Cyber Security, Universiti Teknikal Malaysia Melaka, Malaysia

Received: 23 April 2026 Revised: 10 June 2026 Accepted: 11 June 2026 Published: 01 July 2026
MSC : 26A33, 34A08, 34A23, 92A25

Tuberculosis remains a major public health challenge because of its long latent period, incomplete vaccine protection, and spatially heterogeneous transmission. This study develops a reaction–diffusion model incorporating vaccination, latent infection, active disease, treatment, recovery, nonlinear transmission, and population movement. Analytical and numerical investigations examine disease persistence, spatial spread, pattern formation, and control strategies. Results show that spatial heterogeneity and mobility can increase disease persistence and generate localized hotspots, transmission corridors, and clustered outbreaks. Numerical simulations demonstrate that interventions targeted at high-transmission areas reduce disease burden more effectively than uniformly distributed controls under the same resource constraints. These findings highlight the importance of spatial structure in tuberculosis dynamics and support geographically targeted vaccination and treatment strategies for improved disease control.
- tuberculosis,
- reaction–diffusion,
- Holling type Ⅱ incidence,
- spatial heterogeneity,
- Turing instability,
- optimal control,
- BCG vaccination
Citation: Olumuyiwa James Peter, Azhar Iqbal Kashif Butt, Sharifah Sakinah Syed Ahmad, Fatemah H. H. Al Mukahal. Spatial heterogeneity and nonlinear transmission drive tuberculosis hotspots: a reaction–diffusion modeling study[J]. AIMS Mathematics, 2026, 11(7): 19400-19439. doi: 10.3934/math.2026788

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Abstract

Tuberculosis remains a major public health challenge because of its long latent period, incomplete vaccine protection, and spatially heterogeneous transmission. This study develops a reaction–diffusion model incorporating vaccination, latent infection, active disease, treatment, recovery, nonlinear transmission, and population movement. Analytical and numerical investigations examine disease persistence, spatial spread, pattern formation, and control strategies. Results show that spatial heterogeneity and mobility can increase disease persistence and generate localized hotspots, transmission corridors, and clustered outbreaks. Numerical simulations demonstrate that interventions targeted at high-transmission areas reduce disease burden more effectively than uniformly distributed controls under the same resource constraints. These findings highlight the importance of spatial structure in tuberculosis dynamics and support geographically targeted vaccination and treatment strategies for improved disease control.

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