02097nas a2200241   4500000000100000008004100001260006400042653001800106653003000124653003500154653002800189653002500217653004000242100001100282700001600293700001500309245012100324856006400445300001800509490000700527520130700534022001401841       2026                            d  c10/2026bAmerican Institute of Mathematical Sciences (AIMS)10aleprosy model10areaction-diffusion system10apartial differential equations10aspatiotemporal dynamics10aforward Euler method10aCrank–Nicolson operator splitting1 aKhan A1 aShafiullah 1 aAlqarni AJ00aNumerical simulation of spatiotemporal dynamics of a two-dimensional reaction–diffusion leprosy transmission model  uhttps://www.aimspress.com/article/doi/10.3934/math.20261284  a32714 - 327500 v113 a<p>Leprosy remains one of the biggest public health problems in endemic countries, even with the availability of effective treatments. To better understand how the disease spreads over both time and space, this study extends a standard six-compartment mathematical model into a two-dimensional spatial model using partial differential equations. By including spatial movement (Fickian diffusion), we can simulate how different groups of people interact and move across a given geographical area. We construct two numerical schemes in order to solve this mathematical system: the forward Euler scheme and the Crank–Nicolson operator-splitting method. We analyze the stability properties of both schemes: the forward Euler method is conditionally stable subject to a Courant–Friedrichs–Lewy (CFL) condition, and the Crank–Nicolson operator-splitting method is conditionally stable due to the explicit treatment of the reaction terms, with its diffusion stages being individually unconditionally stable. Moreover, we simulate our mode using MATLAB the long-term stability of the disease. The results of the simulation clearly demonstrate the temporal evolution and geographical spread of leprosy over time, which is a useful tool for public health planning and disease control interventions.</p>
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