Michel Langlais

The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations

Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri‐ or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease‐induced extinction is thus possible for density‐dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond ndocumentclass{aastex}nusepackage{amsbsy}nusepackage{amsfonts}nusepackage{amssymb}nusepackage{bm}nusepackage{mathrsfs}nusepackage{pifont}nusepackage{stmaryrd}nusepackage{textcomp}nusepackage{portland,xspace}nusepackage{amsmath,amsxtra}nusepackage[OT2,OT1]{fontenc}nnewcommandcyr{nrenewcommandrmdefault{wncyr}nrenewcommandsfdefault{wncyss}nrenewcommandencodingdefault{OT2}nnormalfontnselectfont}nDeclareTextFontCommand{textcyr}{cyr}npagestyle{empty}nDeclareMathSizes{10}{9}{7}{6}nbegin{document}nlandscapen

Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion.

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Periodic solutions for a population dynamics problem with age-dependence and spatial structure

nend{document} . This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.

Impacts of plant growth and architecture on pathogen processes and their consequences for epidemic behaviour

On etudie le comportement asymptotique des solutions bornees des equations de la forme u t -Δη(u)=f(x,u) dans Ω×R + , u(x,o)=u 0 (x) dans Ω,u(x,t)=u 1 (x,t) dans ∂Ω×R + , ou Ω est un domaine borne de R N avec ∂Ω de classe C 2, α, 0

Age-dependent population diffusion with external constraint

In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t→+∞ either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.

A modelling approach to vaccination and contraception programmes for rabies control in fox populations

Feline panleucopenia virus (FPLV) was introduced in 1977 on Marion Island (in the southern Indian Ocean) with the aim of eradicating the cat population and provoked a huge decrease in the host population within six years. The virus can be transmitted either directly through contacts between infected and healthy cats or indirectly between a healthy cat and the contaminated environment: a specific feature of the virus is its high rate of survival outside the host. In this paper, a model was designed in order to take these two modes of transmission into account. The results showed that a mass-action incidence assumption was more appropriate than a proportionate mixing one in describing the dynamics of direct transmission. Under certain conditions the virus was able to control the host population at a low density. The indirect transmission acted as a reservoir supplying the host population with a low but sufficient density of infected individuals which allowed the virus to persist. The dynamics of the infection were more affected by the demographic parameters of the healthy hosts than by the epidemiological ones. Thus, demographic parameters should be precisely measured in field studies in order to obtain accurate predictions. The predicted results of our model were in good agreement with observations.

Simulation of rabies control within an increasing fox population

Using a linear model with age-dependence and spatial structure we show how a periodical supply of individuals will transform an exponentially decaying distribution of population into a non-trivial asymptotically stable periodic distribution. Next we give an application to an epidemic model.

Seasonal and spatial heterogeneities in host and vector abundances impact the spatiotemporal spread of bluetongue

As any epidemic on plants is driven by the amount of susceptible tissue, and the distance between organs, any modification in the host population, whether quantitative or qualitative, can have an impact on the epidemic dynamics. In this paper we examine using examples described in the literature, the features of the host plant and the use of crop management which are likely to decrease diseases. We list the pathogen processes that can be affected by crop growth and architecture modifications and then determine how we can highlight the principal ones. In most cases, a reduction in plant growth combined with an increase in plant or crop porosity reduces infection efficiency and spore dispersal. Experimental approaches in semi-controlled conditions, with concomitant characterisation of the host, microclimate and disease, allow a better understanding and analysis of the processes impacted. Afterwards, the models able to measure and predict the effect of plant growth and architecture on epidemic behaviour are reviewed.