Plastic energy allocation toward life-history functions in a consumer-resource interaction : Analyzing the temporal patterns of the consumer-resource dynamics.

Various environmental alterations resulting from the current global change compromise the persistence of species in their habitual environment. To cope with the obvious risk of extinction, plastic responses provide organisms with rapid acclimatization to new environments. The premise of plastic rescue has been theoretically studied from mathematical models in both deterministic and stochastic environments, focusing on analyzing the persistence and stability of the populations. Here, we evaluate this premise in the framework of a consumer-resource interaction considering the energy investment towards reproduction vs. maintenance as a plastic trait according to positive/negative variation of the available resource. A basic consumer-resource mathematical model is formulated based on the principle of biomass conversion that incorporates the energy allocation toward vital functions of the life-cycle of consumer individuals. Our mathematical approach is based on the impulsive differential equations at fixed moments considering two impulsive effects associated with the instants at which consumers obtain environmental information and when energy allocation strategy change occurs. From a preliminary analysis of the non-plastic temporal dynamics, namely when the energy allocation is constant over time and without experiencing changes concerning the variation of resources, both the persistence and stability of the consumer-resource dynamic are dependent on the energy allocation strategies belonging to a set termed stability range. We found that the plastic energy allocation can promote a stable dynamical pattern in the consumer-resource interaction depending on both the magnitude of the energy allocation change and the time lag between environmental sensibility instants and when the expression of the plastic trait occurs.

Número de casos COVID-19 en Chile a 120 días con datos al 21/03/2020 y umbral del esfuerzo diario para aplanar la epi-curva / Number of COVID-19 cases in Chile at 120 days with data at 21/03/2020 and threshold of daily effort to flatten the epi-curve

Realizamos una prospectiva básica, con datos al 21/03/2020 de la evolución del número de casos COVID-19 diarios en Chile con datos del Ministerio de Salud. Asumiendo un crecimiento aritmético en la segunda variación de los datos, se presenta un modelo de ajuste cúbico que estima en más de 100 mil casos a 120 días y que es consistente con los datos registrados a la fecha. Además, se interviene un modelo de casos totales exponencial, para representar en él (mediante un parámetro) el esfuerzo diario por rebajar una elevada primera tasa de crecimiento diario. Este modelo se simula con distinto escenarios numéricos de factibilidad y prevalencia futura deseada.

We present a straightforward projection with data up to 21/03/2020 of the evolution of the number of COVID-19 cases per day in Chile using data from the Ministry of Health. Assuming an arithmetical growth in the second variation of the data, we present a cubic adjustment model in which we estimate over 100 000 cases at 120 days consistent with the data recorded to date. Furthermore, we use an exponential total case model to represent (using a parameter) the daily effort to reduce a high initial daily growth rate. We simulate this model with different numerical scenarios of feasibility and desired future prevalence.

Susceptibility to organophosphates pesticides and the development of infectious-contagious respiratory diseases.

In this paper we develop an SIRS compartmental model to investigate the dynamic interplay between pesticide intoxication and the spread of infectious-contagious respiratory diseases. We are particularly interested in investigating three levels of genetic susceptibility to pesticide intoxication. The genotypic distribution of susceptibility to pesticide intoxication, is proposed and parameterized according to ethnic variation using real population data from published studies, and we assume that pesticide intoxication increases susceptibility to infection with a respiratory pathogen. We use mathematical models to illustrate the impact of this distribution on the spread of hypothetical respiratory disease in a population exposed to the organophosphate pesticide. In this context, we show how an initial basic reproductive number below the epidemic threshold of 1.0 could be enhanced to support epidemic outbreaks in agricultural populations that employ chlorpyrifos pesticides. We further illustrate our modeling framework to study the effect of ethnic group variation in Singapore (Malay, Indian and Chinese) using genetic distribution data from published studies.

Dynamics between infectious diseases with two susceptibility conditions: A mathematical model.

This paper presents a novel epidemiological transmission model of a population affected by two different susceptible-infected-susceptible infectious diseases. For each disease, individuals fall into one of the two susceptibility conditions in which one of the diseases has the highest occurrence level. This model is unique in assuming that: (a) if an individual is infected by one disease, their susceptibility to the other disease is increased; (b) when an individual recovers from a disease they become less susceptible to it, i.e. they acquire partial immunity. The model captures these two assumptions by utilizing a coupled system of differential equations. Dynamic analysis of the system is based on basic reproductive number theory, and pattern visualization was performed using numerical simulation.

Modelización del impacto epidemiológico de la existencia de un grupo conductual preventivo / Modeling the epidemiological impact of a preventive behavioral group

En lo que concierne a salud, la experiencia indica que en toda población humana existe un porcentaje de individuos que se comporta en forma consciente ante la presencia de enfermedades infectocontagiosas. Esto implica que existen grupos con una orientación hacia la prevención en sus actividades para atenuar el riego, mientras que en general la mayoría lo hace distraídamente. La excepción la constituyen los casos de orden catastrófico. Asumiendo el marco teórico y metodológico que otorga la epidemiología matemática, se evaluaron los factores tamaño e intensidad de la conducta del grupo cuidadoso en la determinación del número reproductivo básico, basándose en un modelo tipo SIR (susceptibles - infecciosos - recuperados). Es decir, se midió la reducción en la cantidad de casos secundarios que produciría un primer caso infeccioso. Junto con estos indicadores, se procedió a evaluar la prevalencia evitada total e individual por cada sujeto cuidadoso en diferentes escenarios paramétricos. Finalmente, se plantea la necesidad de integrar en futuros estudios la variable distancia y el contacto interpersonal como factores asociados al potencial de transmisión.

Concerning health, experience indicates that in all human groups a percentage of individuals behave conscientiously when facing contagious diseases. This aware group responds with activities to prevent disease transmission and to minimize risk. In contrast, other individuals tend to behave with less engagement except in catastrophic cases. Assuming the theoretical and methodological framework provided by mathematical epidemiology, and based on a Susceptible ­ Infectious - Recovered (SIR) model, we evaluated the factors of size and intensity of the behaviours in the aware group to determine the basic reproduction number. This number is the reduction in the number of secondary cases that would be produced by a first infectious individual. Additionally, we calculated the total and individual prevented prevalence for each aware individual for different parametric scenarios. Lastly, we suggest that distance and interpersonal contact should be included as factors associated to the potential of transmission.