Front Propagation of Exponentially Truncated Fractional-Order Epidemics

The existence of landscape constraints in the home range of living organisms that adopt Levy-flight movement patterns, prevents them from making arbitrarily large displacements. Their random movements indeed occur in a finite space with an upper bound. In order to make realistic models, by introducing exponentially truncated Levy flights, such an upper bound can thus be taken into account in the reaction-diffusion models. In this work, we have investigated the influence of the lambda-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where lambda is the truncation parameter. Analytical and numerical simulations show that depending on the value of lambda, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of lambda (lambda greater than or similar to 0), the tails of the infective waves can decay algebraically leading to an exponential growth of the epidemic speed. In that case, the truncation has no impact on the superdiffusive epidemics. By increasing the value of lambda, the algebraic decaying tails can be tamed leading to either an upper bound on the epidemic speed representing the maximum speed value or the generation of the infective waves of a constant shape propagating at a minimum constant speed as observed in the classical models (second-order diffusion epidemic models). Our findings suggest that the truncated fractional-order diffusion equations have the potential to model the epidemics of animals performing Levy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics.

Automated summary

This study investigates the influence of the lambda-truncated fractional-order diffusion operator on the spatial propagation of epidemics caused by infectious diseases. The results show that different asymptotic behaviors of the travelling-wave solutions can be identified depending on the value of lambda.