A multi-strain epidemic model for COVID-19 with infected and asymptomatic cases: Application to French data.

Many SARS-CoV-2 variants have appeared over the last months, and many more will continue to appear. Understanding the competition between these different variants could help make future predictions on the evolution of epidemics. In this study we use a mathematical model to investigate the impact of three different SARS-CoV-2 variants on the spread of COVID-19 across France, between January-May 2021 (before vaccination was extended to the full population). To this end, we use the data from Geodes (produced by Public Health France) and a particle swarm optimisation algorithm, to estimate the model parameters and further calculate a value for the basic reproduction number R0. Sensitivity and uncertainty analysis is then used to better understand the impact of estimated parameter values on the number of infections leading to both symptomatic and asymptomatic individuals. The results confirmed that, as expected, the alpha, beta and gamma variants are more transmissible than the original viral strain. In addition, the sensitivity results showed that the beta/gamma variants could have lead to a larger number of infections in France (of both symptomatic and asymptomatic people).

A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers' Migration.

Metaecoepidemic models generalize metapopulation systems, combining local population dynamics with inter-patch migration coupled with an epidemic proliferation. A resource-consumer model is introduced with an ecosystem composed by two patches, in which consumers can freely move. A disease affects resources of the second patch. This situation corresponds to a grassland-herbivore environment, where one patch, managed in an extensive way, has a wider plant diversity, while the other one is highly fertilized leading to an important forage production. The latter is also subject to a fungal disease. Herbivores both feed on healthy or infected crop and can freely migrate between the two patches. A preliminary investigation focuses on behaviors emerging from some parts of the model, respectively, formed by uncoupled patches and by the purely demographic coupled model. Equilibria of the whole system are assessed and characterized. Results are then compared with the purely demographic model to highlight the role of the disease in this dynamics. A thorough numerical investigation of the model completes this analysis to assess the system behavior near each equilibrium. System bifurcations have also been explored as well as the response of the system equilibria to parameter perturbations. The disease eradication is possible under suitable circumstances. Coexistence of the five populations through persistent oscillations is also possible, but it is not at a stable level.

Mathematical modelling and numerical simulations of the influence of hygiene and seasons on the spread of cholera.

Cholera is a bacterial disease, its spread is strongly influenced by environmental factors and some socio-economic factors such as hygiene standards and nutrition of the population. This paper is devoted to the modelling of the impact of climatic factors and human behaviour on the spread of cholera. The mathematical modelling incorporates the direct transmission and the indirect transmission due to environmental knowledge. Taking into account the effect of the intra-annual variation of climatic factors on the transmission of cholera, a non-autonomous ordinary differential equations is proposed to describe the dynamics of the transmission of cholera. When the intra-annual variation of climate is not incorporated into the model, the latter becomes autonomous. The basic reproductive number is calculated and the stabilities of equilibria are investigated. In the non-autonomous case, the disease extinction and uniform persistence of disease are investigated. The results suggest that the transmission and spread of cholera can be affected by climatic factors, the proportion of the undernourished individuals and the proportion of people who respect the hygiene standards. Finally, some numerical simulations are proposed using the parameters values of climatic factors and socio-economic factors of some localities situated in Lake Chad border between Chad, Cameroon and Nigeria.

The adaptation of generalist predators' diet in a multi-prey context: insights from new functional responses.

The ability for a generalist consumer to adapt its foraging strategy (the multi-species functional response, MSFR) is a milestone in ecology as it contributes to the structure of food webs. The trophic interaction between a generalist predator, as the red fox or the barn owl, and its prey community, mainly composed of small mammals, has been empirically and theoretically widely studied. However, the extent to which these predators adapt their diet according to both multi-annual changes in multiple prey species availability (frequency dependence) and the variation of the total prey density (density dependence) is unexplored.We provide a new general model of MSFR disentangling changes in prey preference according to variation of prey frequency (switching) and of total prey density (we propose the new concept of "rank switching"). We apply these models to two large data sets of red fox and barn owl foraging. We show that both frequency-dependent and density-dependent switching are critical properties of these two systems, suggesting that barn owl and red fox have an accurate image of the prey community in terms of frequency and absolute density. Moreover, we show that negative switching, which can lead to prey instability, is a strong property of the two systems.

Competence of hosts and complex foraging behavior are two cornerstones in the dynamics of trophically transmitted parasites.

Multi-host trophically transmitted parasite (TTP) is a common life cycle where prey and predators are respectively intermediate and definitive hosts of the parasite. In these systems, the foraging response of the predator toward variations in prey community composition underlies the dynamic of the parasite. Therefore, modeling epidemiological dynamic of infectious diseases considering ecological predator-prey interactions is essential to understand the spreading of parasites in ecosystems. However, two important weaknesses of previous TTP models including feeding interaction can be pointed out: (i) the choice of a linear density-dependent contact rate is faintly realistic as it supposes an unlimited ingestion rate with an increase of prey density and (ii) considering only one host prey species prevents the study of host biodiversity effect due to change in the prey community composition where species have different competences to be infected and to transmit the parasite. This article attempts to address the dynamics of parasite in a context of multiple intermediate hosts differentiated by their competences and of complex foraging behavior of the predator. We present and analyze a deterministic one predator-two prey model, which is then used to explore the transmission cycle of the cestode Echinococcus multilocularis. This study examines the foraging condition for the co-existence of the prey, and then, based on the computation of the threshold measure of disease risk, R0, we show that the pattern of feeding interactions changes the relationship between disease risk and prey community composition. Finally, we disentangle the mechanism leading to the counter-intuitive observation of a decrease of disease risk while the population density of intermediate hosts increases.