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The evolution of influenza A virus is linked to a non-fixed evolutionary landscape driven by tight co-evolutionary interactions between hosts and influenza strains. Herd-immunity, cross-immunity and age-structure are among the factors shown to support the coexistence of multiple strain oscillations. In this study, we incorporate two influenza strains and(More)
In this paper, a two-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the two strains eliminate each other with the strain with the larger immunological reproduction persisting. However, on the population scale superinfection is possible, with the strain with larger immunological(More)
A classical epidemiological framework is used to provide a preliminary cost analysis of the effects of quarantine and isolation on the dynamics of infectious diseases for which no treatment or immediate diagnosis tools are available. Within this framework we consider the cost incurred from the implementation of three types of dynamic control strategies.(More)
Mathematical models developed for studying malaria dynamics often focus on a single, homogeneous population. However, human movement connects environments with potentially different malaria transmission characteristics. To address the role of human movement and spatial heterogeneity in malaria transmission and malaria control, we consider a simple malaria(More)
In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to(More)
Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the(More)
To better understand the mechanisms involved in the dynamics of Johne's disease in dairy cattle, this paper illustrates a novel way to link a within-host model for Mycobacterium avium ssp. paratuberculosis with an epidemiological model. The underlying variable in the within-host model is the time since infection. Two compartments, infected macrophages and T(More)
This article focuses on the study of an age-structured two-strain model with super-infection. The explicit expression of basic reproduction numbers and the invasion reproduction numbers corresponding to strain one and strain two are obtained. It is shown that the infection-free steady state is globally stable if the basic reproductive number R(0) is below(More)
In this paper, a model for the use of heroin with treat-age is formulated based on the principles of mathematical epidemiology. The model accounts for relapse rate that depends on how long the host has been in treatment for heroin addiction. An explicit formula for the reproductive number of the heroin spread is obtained. By using the method of Lyapunov(More)