A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading

We propose an SIRS compartmental model with demography and fast information and misinformation spreading in the population. The analysis of the complete 6-dimensional system shows the existence of seven equilibrium points. Since under our assumptions the system evolves on two time scales, we completely characterize the possible asymptotic behaviours with techniques of Geometric Singular Perturbation Theory (GSPT). During our analysis of the fast dynamics, we identify three branches of the critical manifold, which exist under determined conditions. We perform a theoretical bifurcation analysis of the fast system to understand the relation between these three equilibria when varying specific parameters of the fast system. We then observed a delayed loss of stability on the various branches of the critical manifold, as the slow dynamics may cause the branches to lose their hyperbolicity. We emphasise how the inclusion of (mis)information spreading, even in low dimensional compartmental models, can radically alter the asymptotic behaviour of the epidemic. We conclude with numerical simulations of various remarkable scenarios.Comment: 27 pages, 8 figures, 1 tabl

Comparing disease control policies for interacting wild populations

We consider interacting population systems of predator-prey type, presenting four models of control strategies for epidemics among the prey. In particular to contain the transmissible disease, safety niches are considered, assuming they lessen the disease spread, but do not protect prey from predators. This represents a novelty with respect to standard ecosystems where the refuge prevents predators' attacks. The niche is assumed either to protect the healthy individuals, or to hinder the infected ones to get in contact with the susceptibles, or finally to reduce altogether contacts that might lead to new cases of the infection. In addition a standard culling procedure is also analysed. The effectiveness of the different strategies are compared. Probably the environments providing a place where disease carriers cannot come in contact with the healthy individuals, or where their contact rates are lowered, seem to preferable for disease containment

Modeling the interactions among phythopatogens and phyllosphere microorganisms for the biological disease control of Olea europaea L.

In this paper we formulate a model for assessing the interaction between the phytopathogen Spilocaea oleaginea and the phyllosphere microorganisms that are present in the olive tree leaves. The model describes the evolution in time of the foliage of the olive tree and the two different microorganisms, the phytopathogen fungi, that negatively affect the plant causing spots in the leaves, and the beneficial phyllosphere microorganisms, that help in keeping in check the invasion of the former. The system possesses five equilibria that are suitably analysed for feasibility and stability. The model shows interesting features: a bistable behavior, exhibited by three different pairs of equilibria. The separatrix surface of the basins of attraction of one such pair is computed. This allows the possible assessment of human intervention for control of the disease. Persistent oscillations via Hopf bifurcation are also discovered.EV and IMB have been partially supported by the projects “Metodi numerici in teoria delle popolazioni” and “Metodi numerici nelle scienze applicate” of the Dipartimento di Matematica “Giuseppe Peano” of the Università di Torino. IMB has been partially supported by ”Finanziamento GNCS Giovani Ricercatori 2016”.info:eu-repo/semantics/publishedVersio