Disease-induced stabilization of predator–prey oscillations

Ecoepidemic modeling and dynamics of alveolar echinococcosis transmission

Alveolar echinococcosis, transmitted between definitive hosts and intermediate hosts via predation, threatens the health of humans and causes great economic losses in western China. In order to explore the transmission mechanism of this disease, an eco-epidemiological lifecycle model is formulated to illustrate interactions between two hosts. The basic and demographic reproduction numbers are developed to characterize the stability of the disease-free and endemic equilibria as well as bifurcation dynamics. The existence of forward bifurcation and Hopf bifurcation are confirmed and are used to explain the threshold transmission dynamics. Numerical simulations and bifurcation diagrams are also presented to depict rich dynamics of the model. Numerical analysis suggests that improving the control rate of voles will reduce the risk of transmission, while the high predation rate of foxes may also lead to a lower transmission risk, which is different from the predictions of previous studies. The evaluation of three control measures on voles implies that, when the fox's predation rate is low (high), the chemical (integrated) control will be more effective.

Pathogens stabilize or destabilize depending on host stage structure

A common assumption is that pathogens more readily destabilize their host populations, leading to an elevated risk of driving both the host and pathogen to extinction. This logic underlies many strategies in conservation biology and pest and disease management. Yet, the interplay between pathogens and population stability likely varies across contexts, depending on the environment and traits of both the hosts and pathogens. This context-dependence may be particularly important in natural consumer-host populations where size- and stage-structured competition for resources strongly modulates population stability. Few studies, however, have examined how the interplay between size and stage structure and infectious disease shapes the stability of host populations. Here, we extend previously developed size-dependent theory for consumer-resource interactions to examine how pathogens influence the stability of host populations across a range of contexts. Specifically, we integrate a size- and stage-structured consumer-resource model and a standard epidemiological model of a directly transmitted pathogen. The model reveals surprisingly rich dynamics, including sustained oscillations, multiple steady states, biomass overcompensation, and hydra effects. Moreover, these results highlight how the stage structure and density of host populations interact to either enhance or constrain disease outbreaks. Our results suggest that accounting for these cross-scale and bidirectional feedbacks can provide key insight into the structuring role of pathogens in natural ecosystems while also improving our ability to understand how interventions targeting one may impact the other.

Impact of different destocking strategies on the resilience of dry rangelands

Half of the world's livestock live in (semi-)arid regions, where a large proportion of people rely on animal husbandry for their survival. However, overgrazing can lead to land degradation and subsequent socio-economic crises. Sustainable management of dry rangeland requires suitable stocking strategies and has been the subject of intense debate in the last decades. Our goal is to understand how variations in stocking strategies affect the resilience of dry rangelands. We describe rangeland dynamics through a simple mathematical model consisting of a system of coupled differential equations. In our model, livestock density is limited only by forage availability, which is itself limited by water availability. We model processes typical of dryland vegetation as a strong Allee effect, leading to bistability between a vegetated and a degraded state, even in the absence of herbivores. We study analytically the impact of varying the stocking density and the destocking adaptivity on the resilience of the system to the effects of drought. By using dynamical systems theory, we look at how different measures of resilience are affected by variations in destocking strategies. We find that the following: (1) Increasing stocking density decreases resilience, giving rise to an expected trade-off between productivity and resilience. (2) There exists a maximal sustainable livestock density above which the system can only be degraded. This carrying capacity is common to all strategies. (3) Higher adaptivity of the destocking rate to available forage makes the system more resilient: the more adaptive a system is, the bigger the losses of vegetation it can recover from, without affecting the long-term level of productivity. The first two results emphasize the need for suitable dry rangeland management strategies, to prevent degradation resulting from the conflict between profitability and sustainability. The third point offers a theoretical suggestion for such a strategy.

Asymmetric host movement reshapes local disease dynamics in metapopulations

Understanding how the movement of individuals affects disease dynamics is critical to accurately predicting and responding to the spread of disease in an increasingly interconnected world. In particular, it is not yet known how movement between patches affects local disease dynamics (e.g., whether pathogen prevalence remains steady or oscillates through time). Considering a set of small, archetypal metapopulations, we find three surprisingly simple patterns emerge in local disease dynamics following the introduction of movement between patches: (1) movement between identical patches with cyclical pathogen prevalence dampens oscillations in the destination while increasing synchrony between patches; (2) when patches differ from one another in the absence of movement, adding movement allows dynamics to propagate between patches, alternatively stabilizing or destabilizing dynamics in the destination based on the dynamics at the origin; and (3) it is easier for movement to induce cyclical dynamics than to induce a steady-state. Considering these archetypal networks (and the patterns they exemplify) as building blocks of larger, more realistically complex metapopulations provides an avenue for novel insights into the role of host movement on disease dynamics. Moreover, this work demonstrates a framework for future predictive modelling of disease spread in real populations.

Infected food web and ecological stability

Parasites are widespread in nature. Nevertheless, they have only recently been incorporated into food web studies and community ecology. Earlier studies revealed the large effects of parasites on food web network structures, suggesting that parasites affect food web dynamics and their stability. However, our understanding of the role of parasites in food web dynamics is limited to a few theoretical studies, which only assume parasite-induced mortality or virulence as a typical characteristic of parasites, without any large difference in terms of predation effects. Here, I present a food web model with parasites in which parasites change the mortality and interaction strengths of hosts by affecting host activity. The infected food web shows that virulence and infection rate have virtually no effect on food web stability without any difference in interaction strengths between susceptible and infected individuals. However, if predation rates are weakened through a restriction of the activity of infected individuals, virulence and infection rate can greatly influence stability: diseases with lower virulence and higher transmission rate tend to increase stability. The stabilization is stronger in cascade than random food webs. The present results suggest that parasites can greatly influence food web stability if parasite-induced diseases prevent host foraging activity. Parasite-induced infectious disease, by weaking species interactions, may play a key role in maintaining food webs.

Night-Restricted Feeding Improves Gut Health by Synchronizing Microbe-Driven Serotonin Rhythm and Eating Activity-Driven Body Temperature Oscillations in Growing Rabbits

The circadian misalignment of the gut microbiota caused by unusual eating times in adult animals is related to disease development. However, whether the composition and diurnal rhythm of gut microbiota can be optimized by synchronizing the window period of eating with natural eating habits to reduce the risk of diarrhea remains unclear, especially in growing animals. In this study, 108 5-week-old weaned rabbits (nocturnal animals) were randomly subjected to daytime feeding (DF) and night-restricted feeding (NRF). At age 12 weeks, six rabbits were selected from each group, and caecum and cecal contents, as well as serum samples were collected at 4-h intervals during 24 h. Overall, NRF was found to reduce the risk of diarrhea in growing rabbits, improved the diurnal rhythm and abundance of beneficial microorganisms, along with the production of beneficial metabolites, whereas reduced the abundance of potential pathogens (Synergistes, Desulfovibrio, and Alistipes). Moreover, NRF improved diurnal rhythm of tryptophan hydroxylase isoform 1 and serotonin. Furthermore, NRF strengthened the diurnal amplitude of body core temperature, and promoted the diurnal expression of intestinal clock genes (BMAL1, CLOCK, REV-ERBα, and PER1), and genes related to the regulation of the intestinal barrier (CLAUDIN-1), and intestinal epithelial cell self-proliferation and renewal (BMI1). In vitro simulation experiments further revealed that synchronization of microbial-driven serotonin rhythm and eating activity-driven body temperature oscillations, which are important zeitgebers, could promote the diurnal expression of clock genes and CLAUDIN-1 in rabbit intestinal epithelial cells (RIEC), and enhance RIEC proliferation. This is the first study to reveal that NRF reprograms the diurnal rhythm of the gut microbiome, promotes the diurnal expression of clock genes and tight junction genes via synchronization of microbial-driven serotonin rhythm and eating activity-driven body temperature oscillations, thereby improving intestinal health and reducing the risk of diarrhea in growing rabbits. Collectively, these results provide a new perspective for the healthy feeding and management of growing animals.

Modeling anthrax-rabies interactions in zebra-jackal cycles

Etosha National Park (ENP) is located in Namibia, where an annual anthrax outbreak (caused by Bacillus anthracis) occurs among grazing animals such as zebras. This increases the number of carcasses in ENP, allowing for scavengers such as jackals to feed off these carcasses. Carcasses provide a location of conspecific interaction between jackals and may be a means of disease transmission among the jackals. We are interested in studying how a disease in the zebra population may help to propagate a different disease (rabies) in the jackal population since the carcasses are providing a location of interaction between the jackals. We aim to answer the following research question: how do anthrax and rabies affect each other's ability to spread? Standard qualitative analysis techniques distinguished outcomes (stable equilibria) using reproduction numbers as threshold quantities. We found that rabies helps anthrax, and a little anthrax helps rabies invade, but a lot of anthrax prevents rabies by reducing the jackal population through its food source.

Predation shapes the impact of cancer on population dynamics and the evolution of cancer resistance

Cancer is a widespread disease that affects most of the metazoans. However, cancer development is a slow process and, long before causing the death of the individual, may weaken organisms' capacities and impair their interactions with other species. Yet, the impact of cancer development on biotic interactions, and over the dynamics of the whole ecosystem, is still largely unexplored. As well, the feedback of altered biotic interactions on the evolution of resistance against cancer in the context of community ecology has not been investigated. From this new perspective, we theoretically investigate how cancer can challenge expected interaction outcomes in a predator-prey model system, and how, in return, these altered interaction outcomes could affect evolution of resistance mechanism against cancer. First, we demonstrate a clear difference between prey and predator vulnerability to cancer, with cancer having a limited impact on prey populations. Second, we show that biotic interactions can surprisingly lead to a null or positive effect of cancer on population densities. Finally, our evolutionary analysis sheds light on how biotic interactions can lead to diverse resistance levels in predator populations. While its role in ecosystems is mostly unknown, we demonstrate that cancer in wildlife is an important ecological and evolutionary force to consider.

Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference

Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator-prey model with a generalized Holling type functional response - considering in particular the "non-smooth" case. This model can also be used to model an infectious disease where a susceptible population, moves to an infected class, after being infected by the disease. We investigate dynamical properties of the system and derive conditions for the occurrence of saddle-node, transcritical and Hopf-bifurcations. A sufficient condition for finite time extinction of the prey species has also been derived. In addition, we investigate the effect of a prey refuge on the population dynamics of the model and derive conditions such that the prey refuge would yield persistence of the population. We provide additional verification of our analytical results via numerical simulations. Our findings are in accordance with classical experimental results in ecology (Gause, 1934), that show that extinction of predator and prey populations is possible in a finite time period - but that bringing in refuge can effectively yield persistence.

Hopf bifurcation and stability analysis of the Rosenzweig-MacArthur predator-prey model with stage-structure in prey

We consider a stage-structure Rosenzweig-MacArthur model describing the predator-prey interaction. Here, the prey population is divided into two sub-populations namely immature prey and mature prey. We assume that predator only consumes immature prey, where the predation follows the Holling type II functional response. We perform dynamical analysis including existence and uniqueness, the positivity and the boundedness of the solutions of the proposed model, as well as the existence and the local stability of equilibrium points. It is shown that the model has three equilibrium points. Our analysis shows that the predator extinction equilibrium exists if the intrinsic growth rate of immature prey is greater than the death rate of mature prey. Furthermore, if the predation rate is larger than the death rate of predator, then the coexistence equilibrium exists. It means that the predation process on the prey determines the growing effects of the predator population. Furthermore, we also show the existence of forward and Hopf bifurcations. The dynamics of our system are confirmed by our numerical simulations.

Intraguild predation decreases predator fitness with potentially varying effects on pathogen transmission in a herbivore host

Predators and pathogens often regulate the population dynamics of their prey or hosts. When species interact with both their predators and their pathogens, understanding each interaction in isolation may not capture the system's dynamics. For instance, predators can influence pathogen transmission via consumptive effects, such as feeding on infected prey, or non-consumptive effects, such as changing the prey's susceptibility to infection. A prey species' infection status can, in turn, influence predator's choice of prey and have negative fitness consequences for the predator. To test how intraguild predation (IGP), when predator and pathogen share the same prey/host, affects pathogen transmission, predator preference, and predator fitness, we conducted a series of experiments using a crop pest (Pseudoplusia includens), a generalist predator (Podisus maculiventris), and a generalist pathogen (Autographa californica multicapsid nuclear polyhedrovirus, AcMNPV). Using a field experiment, we quantified the effects of consumptive and non-consumptive predators on pathogen transmission. We found that a number of models provided similar fits to the data. These models included null models showing no effects of predation and models that included a predation effect. We also found that predators consumed infected prey more often when choosing between live infected or live healthy prey. Infected prey also reduced predator fitness. Developmental times of predators fed infected prey increased by 20% and longevity decreased by 45%, compared with those that consumed an equivalent number of non-infected prey. While this research shows an effect of the pathogen on intraguild predator fitness, we found no support that predators affected pathogen transmission.

Infection pathology and competition mediate host biomass overcompensation from disease

Predators can increase the biomass of their prey, particularly when prey life stages differ in competitive ability and predation is stage specific. Akin to predators, parasites influence host population sizes and engage in stage-structured interactions, yet whether parasites can increase host population biomass remains relatively unexplored. Using a stage-structured consumer-resource model and a mesocosm experiment with snails and castrating trematodes, we examined responses of host biomass to changes in infection prevalence under variation in host pathology and resource competition. Equilibrium adult host biomass increased with infection prevalence in the model when parasites castrated hosts and adults were superior competitors to juveniles. Juvenile biomass increased with infection prevalence whether parasites caused mortality or castration, but only when juveniles were superior competitors. In mesocosms, increases in infection by castrating trematodes reduced snail egg production, juvenile abundance, and adult survival. At high competition, juvenile growth and total biomass increased with infection prevalence due to competitive release. At low competition, juvenile biomass decreased with infection due to reduced reproduction. These results highlight how disease-induced biomass overcompensation depends on infection pathology, resource availability, and competitive interactions within and between host life stages. Considering such characteristics may benefit biocontrol efforts using parasites.

Consumer-resource coexistence as a means of reducing infectious disease

Maintaining sustainable ecosystems are important for all the inhabitants of earth. Also, an important component of sustainable ecosystems is the maintenance of healthy coexistence of consumers and their resources which can include diseases in the species involved. We formulate a model, where the resources are plants, to explore how consumer-resource coexistence could of itself limit the spread of infectious diseases. The important mathematical features of the model are discussed using the basic reproduction number and the consumption number. The results show an association between species coexistence and a decrease in ecosystem resource disease. The possible importance of these results are discussed.

Eco-epidemiological interactions with predator interference and infection

Predator interference is a form of competition between predator individuals over access to their prey. There is broad empirical evidence for interference to exist in different strengths in various types of ecological communities. At the same time, parasites are increasingly recognized to alter food web structure and dynamics. In order to investigate the eco-epidemiological interplay between interference and infection, we develop and analyze mathematical models of a predator-prey system, where the predators are subject to both interference and infectious disease. In the absence of infection, equilibrium predator density is known to show a non-monotonic response to interference by first increasing and then decreasing with increasing interference levels. We show that predator infection can change this pattern into a monotonically decreasing predator response to interference, provided the transmissibility is large enough and the pathogenicity is moderate such that the impact of disease on host population density prevails over interference effects. This holds for both types of disease transmission studied here, density-dependent and frequency-dependent. For density-dependent transmission, we find that intermediate values of interference can facilitate disease persistence, whereas the disease would disappear for small or large interference levels. By contrast, for frequency-dependent transmission, disease emergence is independent of interference levels. These dynamic interactions may be important for the understanding of potential biocontrol measures and of spread patterns of zoonotic diseases.

Indirect effects in a planktonic disease system

Indirect effects, both density- and trait-mediated, have been known to act in tandem with direct effects in the interactions of numerous species. They have been shown to affect populations embedded in competitive and mutualistic networks alike. In this work, we introduce a four-dimensional system of ordinary differential equations and investigate the interplay between direct density-effects and density- and trait-mediated indirect effects that take place in a yeast parasite-zooplankton host-incompetent competitor system embedded in a food web which also includes resources and predators. Among our main findings is the demonstration that indirect effects cause qualitative and quantitative changes almost indistinguishable from direct effects and the corroboration through our analysis of the fact that the effects of direct and indirect mechanisms cannot be disentangled. Our results underpin the conclusions of past studies calling for comprehensive models that incorporate both direct and indirect effects to better describe field data.

The Impact of Selective Predation on Host-Parasite SIS Dynamics

While models of host-parasite interactions are widespread in the theoretical literature, we still have limited understanding of the impact of community dynamics on infectious disease dynamics. When the wider host ecology is taken into account, the underlying inter-species feedbacks can lead to counter-intuitive results. For example, the 'healthy herd' hypothesis posits that the removal of a predator species may not be beneficial for a prey population infected by an endemic disease. In this work, we focus on the effects of including a predator species in a susceptible-infected-susceptible model. Specifically, a key role is played by predator selectivity for either healthy or infected prey. We explored both cases and found important differences in the asymptotic behaviours of the system. Independently from selectivity, large portions of parameter space allow for the coexistence of the three species. However, when predators feed mainly on susceptible prey we find that a fold bifurcation can occur, leading to a region of bi-stability between coexistence and parasite extinction. Conversely, when predator selection is strongly towards infected prey, total prey population density can be maximal when the three species coexist, consistent with the 'healthy herd' hypothesis. Our work further highlights the importance of community interactions to infectious disease dynamics.

Effect of copper contamination on zooplankton epidemics

Infectious disease and chemical contamination are increasingly becoming vital issues in many ecosystems. However, studies integrating the two are surprisingly rare. Contamination not only affects the inherent host-resource interaction which influences the epidemic process but may also directly affect epidemiological traits via changes in host's behaviour. The fact that heavy metal such as copper is also an essential trace element for organisms, further increase complexity which make predicting the resultant effect of contamination and disease spread difficult. Motivated by this, we model the effect of copper enrichment on a phytoplankton-zooplankton-fungus system. We show that extremely deficient or toxic copper may have a destabilizing effect on the underlying host-resource dynamics due to increased relative energy fluxes as a result of low host mortality due to fish predation. Further, on incorporating disease into the system, we find that the system can become disease-free for an intermediate range of copper concentration whereas it may persist for very less copper enrichment. Also, we predict that there may exist vulnerable regions of copper concentration near the toxic and deficient levels, where the parasite can invade the system for a comparatively lower spore yield. Overall, our results demonstrate that, the effect of contamination may be fundamental to understanding disease progression in community ecology.

Resource-driven changes to host population stability alter the evolution of virulence and transmission

What drives the evolution of parasite life-history traits? Recent studies suggest that linking within- and between-host processes can provide key insight into both disease dynamics and parasite evolution. Still, it remains difficult to understand how to pinpoint the critical factors connecting these cross-scale feedbacks, particularly under non-equilibrium conditions; many natural host populations inherently fluctuate and parasites themselves can strongly alter the stability of host populations. Here, we develop a general model framework that mechanistically links resources to parasite evolution across a gradient of stable and unstable conditions. First, we dynamically link resources and between-host processes (host density, stability, transmission) to virulence evolution, using a 'non-nested' model. Then, we consider a 'nested' model where population-level processes (transmission and virulence) depend on resource-driven changes to individual-level (within-host) processes (energetics, immune function, parasite production). Contrary to 'non-nested' model predictions, the 'nested' model reveals complex effects of host population dynamics on parasite evolution, including regions of evolutionary bistability; evolution can push parasites towards strongly or weakly stabilizing strategies. This bistability results from dynamic feedbacks between resource-driven changes to host density, host immune function and parasite production. Together, these results highlight how cross-scale feedbacks can provide key insights into the structuring role of parasites and parasite evolution.This article is part of the theme issue 'Anthropogenic resource subsidies and host-parasite dynamics in wildlife'.

Deterministic and stochastic analysis of an eco-epidemiological model

Chronic wasting disease (CWD) is a contagious prion disease among the deer family that has the potential to disrupt the ecosystems where deer occur in abundance. To understand the dynamics of this emerging infectious disease, we consider a simple eco-epidemic model where the host population is infected by CWD. Boundedness of the system is established. The structure of equilibria and their linearized stability are investigated. The persistence condition is discussed. By constructing a suitable Lyapunov function, we discuss the global stability of the endemic equilibrium. Local bifurcation (transcritical) around the boundary equilibria is developed. Sufficient conditions for the existence of Hopf-bifurcation are derived. Further, we have also introduced white type of noise into the system to investigate stochastic stability. This suggests that the deterministic model is robust with respect to stochastic perturbation. Some numerical simulations are performed to validate our results.

Phytoplasma infection of a tropical root crop triggers bottom-up cascades by favoring generalist over specialist herbivores

Global interest on plant-microbe-insect interactions is rapidly growing, revealing the multiple ways in which microorganisms mediate plant-herbivore interactions. Phytopathogens regularly alter whole repertoires of plant phenotypic traits, and bring about shifts in key chemical or morphological characteristics of plant hosts. Pathogens can also cause cascading effects on higher trophic levels, and eventually shape entire plant-associated arthropod communities. We tested the hypothesis that a Candidatus Phytoplasma causing cassava witches' broom (CWB) on cassava (Manihot esculenta Grantz) is altering species composition of invasive herbivores and their associated parasitic hymenopterans. We conducted observational studies in cassava fields in eastern Cambodia to assess the effect of CWB infection on abundance of specialist and generalist mealybugs (Homoptera: Pseudococcidae), and associated primary and hyper-parasitoid species. CWB infection positively affects overall mealybug abundance and species richness at a plant- and field-level, and disproportionately favors a generalist mealybug over a specialist feeder. CWB phytoplasma infection led to increased parasitoid richness and diversity, with richness of 'comparative' specialist taxa being the most significantly affected. Parasitism rate did not differ among infected and uninfected plants, and mealybug host suppression was not impacted. CWB phytoplasma modifies host plant quality for sap-feeding homopterans, differentially affects success rates of two invasive species, and generates niche opportunities for higher trophic orders. By doing so, a Candidatus phytoplasma affects broader food web structure and functioning, and assumes the role of an ecosystem engineer. Our work unveils key facets of phytoplasma ecology, and sheds light upon complex multi-trophic interactions mediated by an emerging phytopathogen. These findings have further implications for invasion ecology and management.

Diseased Social Predators

Social predators benefit from cooperation in the form of increased hunting success, but may be at higher risk of disease infection due to living in groups. Here, we use mathematical modeling to investigate the impact of disease transmission on the population dynamics benefits provided by group hunting. We consider a predator-prey model with foraging facilitation that can induce strong Allee effects in the predators. We extend this model by an infectious disease spreading horizontally and vertically in the predator population. The model is a system of three nonlinear differential equations. We analyze the equilibrium points and their stability as well as one- and two-parameter bifurcations. Our results show that weakly cooperating predators go unconditionally extinct for highly transmissible diseases. By contrast, if cooperation is strong enough, the social behavior mediates conditional predator persistence. The system is bistable, such that small predator populations are driven extinct by the disease or a lack of prey, and large predator populations survive because of their cooperation even though they would be doomed to extinction in the absence of group hunting. We identify a critical cooperation level that is needed to avoid the possibility of unconditional predator extinction. We also investigate how transmissibility and cooperation affect the stability of predator-prey dynamics. The introduction of parasites may be fatal for small populations of social predators that decline for other reasons. For invasive predators that cooperate strongly, biocontrol by releasing parasites alone may not be sufficient.

Effect of multiple delays on the dynamics of cannibalistic prey–predator system with disease in both populations

In the present paper, we investigate a prey–predator system with disease in both prey and predator populations and the predator population is cannibalistic in nature. The model is extended by introducing incubation delays in disease transmission terms. Local stability analysis of the system around the biologically feasible equilibria is studied. The bifurcation analysis of the system around the interior equilibrium is also studied. The sufficient conditions for the permanence of the system are derived in the presence of delays. We observe that incubation delays have the ability to destabilize the cannibalistic prey–predator system. Finally, we perform numerical experiments to substantiate our analytical findings.

Effects of allochthonous inputs in the control of infectious disease of prey

Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model.

Alternative food and external source of infection stabilize predator–prey oscillations — A conclusion drawn from an eco-epidemiological model

Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95(3) (2009) 188–199] proposed an eco-epidemiological model where the prey species is infected through the external source of infection and contact of the species. In this present study we have modified their model by assuming that the predator consumes both the susceptible as well as the infected prey following the modified Holling type-II functional response. Our main focusing points of this study are the role of infection rate (both internal and external), alternative food, and half-saturation constant in the predator–prey dynamics with disease in the prey population. We have shown the local stability of the boundary as well as the interior equilibrium point under certain conditions. We have also worked out the permanence of the system. Our simulation results show that the system enters into limit cycle oscillations from stable position for higher values of the contact rate. But it is also shown that the external infection rate, enrichment of the alternative food of the predator population and the half-saturation constant can prevent limit cycle oscillations and stabilize the system. Thus external disease propagation, enrichment of the alternative food resource, and the half-saturation constant are the key factors for preventing the oscillatory behavior of the species.

Transmission dynamics of resistant bacteria in a predator-prey system

This paper discusses the impact on human health caused by the addition of antibiotics in the feed of food animals. We use the established transmission rule of resistant bacteria and combine it with a predator-prey system to determine a differential equations model. The equations have three steady equilibrium points corresponding to three population dynamics states under the influence of resistant bacteria. In order to quantitatively analyze the stability of the equilibrium points, we focused on the basic reproduction numbers. Then, both the local and global stability of the equilibrium points were quantitatively analyzed by using essential mathematical methods. Numerical results are provided to relate our model properties to some interesting biological cases. Finally, we discuss the effect of the two main parameters of the model, the proportion of antibiotics added to feed and the predation rate, and estimate the human health impacts related to the amount of feed antibiotics used. We further propose an approach for the prevention of the large-scale spread of resistant bacteria and illustrate the necessity of controlling the amount of in-feed antibiotics used.

A mathematical study of a predator–prey model with disease circulating in the both populations

Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator–prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly (by contact) within the prey population and indirectly (by consumption of infected prey) within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator–prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.

Complex Daphnia interactions with parasites and competitors

Species interactions can strongly influence the size and dynamics of epidemics in populations of focal hosts. The "dilution effect" provides a particularly interesting type of interaction from a biological standpoint. Diluters - other host species which resist infection but remove environmentally-distributed propagules of parasites (spores) - should reduce disease prevalence in focal hosts. However, diluters and focal hosts may compete for shared resources. This combination of positive (dilution) and negative (competition) effects could greatly complicate, even undermine, the benefits of dilution and diluter species from the perspective of the focal host. Motivated by an example from the plankton (i.e., zooplankton hosts, a fungal parasite, and algal resources), we study a model of dilution and competition. Our model reveals a suite of five results: • A diluter that is a superior competitor wipes out the host, regardless of parasitism. Although expected, this outcome is an ever-present danger in strategies that might use diluters to control disease. • If the diluter is an inferior competitor, it can reduce disease prevalence, despite the competition, as parameterized in our model. However, competition may also reduce density of susceptible hosts to levels below that seen in focal host-parasite systems alone. • As they decrease disease prevalence, diluters destabilize dynamics of the focal host and their resources. Thus, diluters undermine the stabilizing effects of disease. • The four species combination can generate very complex dynamics, including period-doubling bifurcations and torus (Neimark-Sacker) bifurcations. • At lower resource carrying capacity, the diluter’s dilution of spores is 'helpful' to the focal host, i.e., dilution can elevate host density by reducing disease. But, as the resource carrying capacity increases further, the equilibrium density of the diluter increases while the density of the focal host decreases, despite competition. Namely, the negative effects of competition start to outweigh the positive effects of dilution from the perspective of equilibrium density of the focal host.

The impact of predation on the coexistence and competitive exclusion of pathogens in prey

A two-strain epidemic model with saturating contact rate under a generalist predator is proposed. For a generalist predator which feeds on many types of prey, we assume that the predator can discriminate among susceptible and infected with each strain prey. First, mathematical analysis of the model with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, persistence and global stability are analyzed. Second, the two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If predation is discriminate, then depending on the predation level, a dominant strain may occur. Thus, for some predation levels, the strain one may persist while for other predation levels strain two may persist. Furthermore, coexistence line and coexistent asymptotic-periodic solution are obtained when coexistence occur while heteroclinic is obtained when the two strains competitively exclude each other. Finally, the impact of predation is mentioned along with numerical results to provide some support to the analytical findings.

Spread of infectious diseases in a hyperbolic reaction-diffusion susceptible-infected-removed model

A one-dimensional hyperbolic reaction-diffusion model of epidemics is developed to describe the dynamics of diseases spread occurring in an environment where three kinds of individuals mutually interact: the susceptibles, the infectives, and the removed. It is assumed that the disease is transmitted from the infected population to the susceptible one according to a nonlinear convex incidence rate. The model, based upon the framework of extended thermodynamics, removes the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models. Linear stability analyses are performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. Emphasis is given to the occurrence of Hopf and Turing bifurcations, which break the temporal and the spatial symmetry of the system, respectively. The existence of traveling wave solutions connecting two steady states is also discussed. The governing equations are also integrated numerically to validate the analytical results and to characterize the spatiotemporal evolution of diseases.

Evolution of pathogen virulence under selective predation: a construction method to find eco-evolutionary cycles

We investigate eco-evolutionary cycles in the joint dynamics of pathogen virulence and predator population density when hosts carrying virulent infections are exposed to increased risk of predation. We introduce a new technique to find trade-off functions under which the model exhibits limit cycles; this technique provides a constructive proof that the system is able to generate limit cycles, and can be applied to other eco-evolutionary models as well. We also study a concrete example to confirm that eco-evolutionary cycles occur in a significant part of the parameter space and to briefly explore other evolutionary outcomes in the same model.

ROLE OF HARVESTING IN CONTROLLING CHAOTIC DYNAMICS IN THE PREDATOR–PREY MODEL WITH DISEASE IN THE PREDATOR

Predator–prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator–prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

An incubating diseased-predator ecoepidemic model

We present a model for transmissible diseases spreading among predators in a predator-prey system. Upon successful contact, a susceptible individual becomes infected but is not yet able to spread the disease further. After an incubation period, the diseased individual becomes infectious. We investigate the system's equilibria by analytical and numerical means. For a suitable set of parameter values, the system shows persistent oscillations. The model also exhibits bistability of the coexistence equilibrium with the prey-only equilibrium.

Mathematical Modeling of Viral Zoonoses in Wildlife

Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.