The effect of time delay in plant-pathogen interactions with host demography

Background: There is a need for valid and comprehensive measures of parental influence on children's energy balance-related behaviours (EBRB). Such measures should be based on a theoretical framework, acknowledging the dynamic and complex nature of interactions occurring within a family. The aim of the Family & Dietary habits (F&D) project was to develop a conceptual framework identifying important and changeable family processes influencing dietary behaviours of 13-15 year olds. A second aim was to develop valid and reliable questionnaires for adolescents and their parents (both mothers and fathers) measuring these processes. Methods: A stepwise approach was used; (1) preparation of scope and structure, (2) development of the F&D questionnaires, (3) the conducting of pilot studies and (4) the conducting of validation studies (assessing internal reliability, test-retest reliability and confirmatory factor analysis) using data from a cross-sectional study. Results: The conceptual framework includes psychosocial concepts such as family functioning, cohesion, conflicts, communication, work-family stress, parental practices and parental style. The physical characteristics of the home environment include accessibility and availability of different food items, while family meals are the sociocultural setting included. Individual characteristics measured are dietary intake (vegetables and sugar-sweetened beverages) and adolescents' impulsivity. The F&D questionnaires developed were tested in a test-retest (54 adolescents and 44 of their parents) and in a cross-sectional survey including 440 adolescents (13-15 year olds), 242 mothers and 155 fathers. The samples appear to be relatively representative for Norwegian adolescents and parents. For adolescents, mothers and fathers, the test-retest reliability of the dietary intake, frequencies of (family) meals, work-family stress and communication variables was satisfactory (ICC: 0.53-0.99). Barratt Impulsiveness Scale-Brief (BIS-Brief) was included, assessing adolescent's impulsivity. The internal reliability (Cronbach's alphas: 0.77/0.82) and test-retest reliability values (ICC: 0.74/0.77) of BIS-Brief were good. Conclusions: The conceptual framework developed may be a useful tool in guiding measurement and assessment of the home food environment and family processes related to adolescents' dietary habits, in particular and for EBRBs more generally. The results support the use of the F&D questionnaires as psychometrically sound tools to assess family characteristics and adolescent's impulsivity

The temporal patterns of disease severity and prevalence in schistosomiasis

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra-and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility. (C) 2015 AIP Publishing LLC

Controllability of an eco-epidemiological system with disease transmission delay: A theoretical study

This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon is obtained and subsequently, we use a normal form method and the center manifold theorem to examine the nature of the Hopf bifurca-tion. It is clearly observed that competition among predators can drive the system to a stable from an unstable state. Also the infection and competition among predator population enhance the availability of prey for harvesting when their values are high. Finally, some numerical simu-lations are carried out to illustrate the analytical results

Seasonality and adaptive dynamics in host-parasite systems in wildlife

I parametri ecologici sono solitamente difficili da stimare nella fauna selvatica, ma, nel caso di malattie infettive, il tasso di trasmissione del patogeno è il processo più complesso da valutare. Tra i tratti caratteristici dell’ospite la taglia corporea è sicuramente il più influente, in quanto molti parametri demografici scalano allometricamente con essa. In questo lavoro ho mostrato come le relazioni allometriche possono legare la taglia dell’ospite al tasso di trasmissione della malattia e al suo tasso netto di riproduzione. Quindi ho analizzato come le dinamiche epidemiologiche variano in funzione della taglia. Inoltre, sotto le stesse ipotesi, ho studiato l’effetto della variazione stagionale di parametri come tasso di trasmissione e natalità, sulla dinamica della malattia. Per quanto riguarda il controllo dell’infezione, ho analizzato l’effetto di politiche di abbattimento in diverse condizioni ecologiche. In particolare, mi sono concentrato sull’efficacia del controllo in presenza di ceppi a diversa virulenza e in presenza di struttura d’età nella popolazione ospite. In entrambi i casi ho trovato che esistono determinate condizioni ecologiche per cui una politica di eradicazione della malattia basata sull’abbattimento può avere conseguenze peggiori dell’alternativa zero. Ho inoltre mostrato in quali condizioni semplici politiche di abbattimento tempo-variante possono migliorare significativamente il controllo della malattia.Ecological parameters are usually hard to estimate correctly in wild populations, but, in the case of infectious diseases, the rate of transmission of the pathogen agent is often the most complex process to evaluate. Of the many traits characterizing host species demography, body size is probably the most influential one, as many demographic parameters scale allometrically with host body size. In this work I show how the allometric relationships, usually found for demographic parameters, may link host body size with the disease transmission rate and its basic reproduction number. Then, I analysed the effect of seasonal variation in different ecological and epidemiological parameters on disease dynamics. Under the point of view of disease control, I analysed the effectiveness of depopulation policies in different ecological conditions. In particular, I focused on control effectiveness when strains with different virulence co-circulate in the host population and when disease transmission is a function of the age/stage class of the host individuals. In both cases, I found that (under certain conditions) culling policies may perform worse, in terms of disease control, than the do-nothing alternative. I also show in which conditions simple time-variant control policies can improve disease control in wildlife

Analysis of stability and Hopf bifurcation for an eco-epidemiological model with distributed delay

In this paper, the dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions for the asymptotical stability of all the equilibria are obtained. We prove that there exists a threshold value of the infection rate $b$ beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore's condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings

Fractional dynamics and recurrence analysis in cancer model

In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by means of the bifurcation diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recurrence rate (RR), the determinism (DET), and the recurrence time entropy (RTE). We find a high correlation coefficient between the Lyapunov exponents and RTE. Our simulations suggest that the tumor growth parameter ($\rho_1$) is associated with a chaotic regime. Our results suggest a high correlation between the largest Lyapunov exponents and RTE. After understanding the dynamics of the model in the standard formulation, we extend our results by considering fractional operators. We fix the parameters in the chaotic regime and investigate the effects of the fractional order. We demonstrate how fractional dynamics can be properly characterized using RQA measures, which offer the advantage of not requiring knowledge of the fractional Jacobian matrix. We find that the chaotic motion is suppressed as $\alpha$ decreases, and the system becomes periodic for $\alpha \lessapprox 0.9966$. We observe limit cycles for $\alpha \in (0.9966,0.899)$ and fixed points for $\alpha<0.899$. The fixed point is determined analytically for the considered parameters. Finally, we discover that these dynamics are separated by an exponential relationship between $\alpha$ and $\rho_1$. Also, the transition depends on a supper transient which obeys the same relationship

Mathematical Modeling and Analysis of Epidemiological and Chemical Systems

This dissertation focuses on three interdisciplinary areas of applied mathematics, mathematical biology/epidemiology, economic epidemiology and mathematical physics, interconnected by the concepts and applications of dynamical systems.;In mathematical biology/epidemiology, a new deterministic SIS modeling framework for the dynamics of malaria transmission in which the malaria vector population is accounted for at each of its developmental stages is proposed. Rigorous qualitative and quantitative techniques are applied to acquire insights into the dynamics of the model and to identify and study two epidemiological threshold parameters reals* and R0 that characterize disease transmission and prevalence, and that can be used for disease control. It is shown that nontrivial disease-free and endemic equilibrium solutions, which can become unstable via a Hopf bifurcation exist. By incorporating vector demography; that is, by interpreting an aspect of the life cycle of the malaria vector, natural fluctuations known to exist in malaria prevalence are captured without recourse to external seasonal forcing and delays. Hence, an understanding of vector demography is necessary to explain the observed patterns in malaria prevalence. Additionally, the model exhibits a backward bifurcation. This implies that simply reducing R0 below unity may not be enough to eradicate the malaria disease. Since, only the female adult mosquitoes involved in disease transmission are identified and fully accounted for, the basic reproduction number (R0) for this model is smaller than that for previous SIS models for malaria. This, and the occurrence of both oscillatory dynamics and a backward bifurcation provide a novel and plausible framework for developing and implementing optimal malaria control strategies, especially those strategies that are associated with vector control.;In economic epidemiology, a deterministic and a stochastic model are used to investigate the effects of determinism, stochasticity, and safety nets on disease-driven poverty traps; that is, traps of low per capita income and high infectious disease prevalence. It is shown that economic development in deterministic models require significant external changes to the initial economic and health care conditions or a change in the parametric structure of the system. Therefore, poverty traps arising from deterministic models lead to more limited policy options. In contrast, there is always some probability that a population will escape or fall into a poverty trap in stochastic models. It is demonstrated that in stochastic models, a safety net can guarantee ultimate escape from the poverty trap, even when it is set within the basin of attraction of the poverty trap or when it is implemented only as an economic or health care intervention. It is also shown that the benefits of safety nets for populations that are close to the poverty trap equilibrium are highest for the stochastic model and lowest for the deterministic model. Based on the analysis of the stochastic model, the following optimal economic development and public health intervention questions are answered: (i) Is it preferable to provide health care, income/income generating resources, or both health care and income/income generating resources to enable populations to break cycles of poverty and disease; that is, escape from poverty traps? (ii) How long will it take a population that is caught in a poverty trap to attain economic development when the initial health and economic conditions are reinforced by safety nets?;In mathematical physics, an unusual form of multistability involving the coexistence of an infinite number of attractors that is exhibited by specially coupled chaotic systems is explored. It is shown that this behavior is associated with generalized synchronization and the emergence of a conserved quantity. The robustness of the phenomenon in relation to a mismatch of parameters of the coupled systems is studied, and it is shown that the special coupling scheme yields a new class of dynamical systems that manifests characteristics of dissipative and conservative systems