On the Supervision of a Saturated SIR Epidemic Model with Four Joint Control Actions for a Drastic Reduction in the Infection and the Susceptibility through Time

This paper presents and studies a new epidemic SIR (Susceptible–Infectious–Recovered) model with susceptible recruitment and eventual joint vaccination efforts for both newborn and susceptible individuals. Furthermore, saturation effects in the infection incidence terms are eventually assumed for both the infectious and the susceptible subpopulations. The vaccination action on newborn individuals is assumed to be applied to a fraction of them while that on the susceptible general population is of linear feedback type reinforced with impulsive vaccination actions (in practice, very strong and massive vaccination controls) at certain time points, based on information on the current levels of the susceptible subpopulation. Apart from the above vaccination controls, it is also assumed that the average of contagion contacts can be controlled via intervention measures, such as confinements or isolation measures, social distance rules, use of masks, mobility constraints, etc. The main objectives of the paper are the achievement of a strictly decreasing infection for all time periods and that of the susceptible individuals over the initial period if they exceed the disease-free equilibrium value. The monitoring mechanism is the combined activation of intervention measures to reduce the contagion contacts together with the impulsive vaccination to reduce susceptibility. The susceptibility and recovery levels of the disease-free equilibrium point are suitably prefixed by the design of the regular feedback vaccination on the susceptible subpopulation.The research received support from the Spanish Government and the European commission through grant RTI2016-094336-BI00 (MCIU/AEI/FEDER, UE)

On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models

This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.This research was funded by MCIU/AEI/FEDER, UE, grant number RTI2018-094902-B-C22 and the APC was funded by RTI2018-094902-B-C22

Exclusion of generalist pathogens in multihost communities

Knowing how to control a pathogen that infects more than one host species is of increasing importance because the incidence of such infections grows with continuing environmental change. Of concern are infections transmitted from wildlife to humans or livestock. To determine which options are available to control a pathogen in these circumstances, we analyze the pathogen invasion matrix for the multihost susceptible-infected-susceptible model. We highlight the importance of both community structure and the column sum or row sum index, an indicator of both force of infection and community stability. We derive a set of guidelines for constructing culling strategies and suggest a hybrid strategy that has the advantages of both the bottom-up and the top-down approaches, which we study in some detail. The analysis holds for an arbitrary number of host species, enabling the analysis of large-scale ecological systems and systems with spatial dimensions. We test the robustness of our methods by making two changes in the structure of the underlying dynamic model, adding direct competition and introducing frequency-dependent infection transmission. In particular, we show that the introduction of an additional host can eliminate the pathogen rather than eliminate the resident host. The discussion is illustrated with a reference to bovine tuberculosis

A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures

Two discrete mathematical SIR models (Susceptible-Infectious-Recovered) are proposed for modelling the propagation of the SARS-CoV-2 (COVID-19) through Spain and Italy. One of the proposed models is delay-free while the other one considers a delay in the propagation of the infection. The objective is to estimate the transmission, also known as infectivity rate, through time taking into account the infection evolution data supplied by the official health care systems in both countries. Such a parameter is estimated through time at different regional levels and it is seen to be strongly dependent on the intervention measures such as the total (except essential activities) or partial levels of lockdown. Typically, the infectivity rate evolves towards a minimum value under total lockdown and it increases again when the confinement measures are partially or totally removed.The authors are grateful to the institute Carlos III for grant COV20/01213, to the Spanish Government for Grants RTI2018- 094336-B-I00 and RTI2018-094902-B-C22 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-19

A Study on COVID-19 Incidence in Europe through Two SEIR Epidemic Models Which Consider Mixed Contagions from Asymptomatic and Symptomatic Individuals

The impact of the SARS-CoV-2 (COVID-19) on the world has been partially controlled through different measures of social isolation and prophylaxis. Two new SEIR (Susceptible-Exposed-Infected-Recovered) models are proposed in order to describe this spread through different countries of Europe. In both models the infectivity of the asymptomatic period during the exposed stage of the disease will be taken into account. The different transmission rates of the SEIR models are calculated by considering the different locations and, more importantly, the lockdown measures implemented in each region. A new classification of these intervention measures will be set and their influence on the values of the transmission rates will be estimated through regression analysis.The authors are grateful to the institute Carlos III for grant COV20/01213, to the Spanish Government for Grants RTI2018-094336-B-I00 and RTI2018-094902-BC22 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-19

Regulating services

No abstract available

Spatial modelling in plant ecology

In this thesis a range of lattice based spatially explicit models of ecosystems are presented and their applicability to various ecological situations is demonstrated with emphasis on plant communities These mechanistic and individual based models which include coupled map lattices and cellular automata aim to produce ecological insights and testable results Models of both short and long term systems are developed with the former being potentially testable in the eld and the latter promoting understanding where experimentation is not feasible A range of graphical and numerical techniques were developed to investigate both plant and animal model ecosystems The starting point is a short term single species coupled map lattice which investigates popula tion structure arising from local competitive interactions The model concludes that increase of size variation with increasing density indicates the presence of competitive intraspecic asymme try This idea is applied to crop data where considerable asymmetry is identied emphasising the need for balancing crop yield and size consistency Multispecies extensions to this model focus on spatial patterning arising from biotic interac tions and various numerical techniques underline the asymmetrical relationship between long and short lived species Environmental heterogeneity is imposed on the plant species in a third version of the model via the incorporation of an explicit resource base The complex inter dependence of community and environment is highlighted and illustrated by a model of the evolution of seed sizes Through the application of cellular automata to forest and epidemiological systems the concept of memory such as age or stage structuring is shown to be vital in the generation of spatial structure in long term ecological systems Analytical investigations generate further insights and again emphasise the crucial role played by spatial extensiveness in the wide range of ecological situations considered here In conclusion lattice models are ideally suited to the study of ecosystem

Spatial Dynamic Models for Fishery Management and Waterborne Disease Control

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no-take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically. Infectious diseases are another area of concern for the human population. Recently, questions have been raised as to the importance of spatial features on disease spread and how movement patterns affect management strategies. The role of spatial arrangements in a metapopulation on the spread and management strategies of a cholera epidemic is investigated. We consider how the movement of individuals and water affects the optimal vaccination strategy. For each metapopulation, the model has an Susceptible-Infected-Recovered (SIR) system of differential equations coupled with an equation modeling the concentration of Vibrio cholerae in an aquatic reservoir. The model is used to compare spatial arrangements and varying scenarios to draw conclusions on how to effectively manage outbreaks. The work is motivated by the recent cholera outbreak in Haiti