Abstract
The existence of landscape constraints in the home range of living organisms that adopt Lévy-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 Lévy 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 λ-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where λ is the truncation parameter. Analytical and numerical simulations show that depending on the value of λ, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of λ (λ≳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 λ, 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 Lévy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics.
Highlights
Infectious pathogens, such as viruses are the microorganisms that can cause infectious diseases following their presence and growth in humans and animals [1]
In this study, we apply the random mobility of infective individuals following truncated Lévy flights to an epidemic model and explore the epidemic speed based on the different values of the truncation parameter
We have investigated the spatial propagation of the epidemics caused by infectious diseases
Summary
Infectious pathogens, such as viruses are the microorganisms that can cause infectious diseases following their presence and growth in humans and animals (hosts) [1]. Considering the random mobility of hosts and the spatial heterogeneity of the environment lead to the reaction-diffusion models that describe the spatial dynamics of infectious diseases [11,12,13]. Considering a population of the walkers performing a Lévy-flight mobility pattern leads to a fractional-order reaction-diffusion equation whose solution represents the walker densities [18,27]. Considering a large number of random walkers performing a truncated Lévy flight leads to a truncated fractional-order diffusion equation whose solution represents the walker densities [44,45]. In this study, we apply the random mobility of infective individuals following truncated Lévy flights to an epidemic model and explore the epidemic speed based on the different values of the truncation parameter.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have