Zoonotic transmission of intestinal helminths in southeast Asia: Implications for control and elimination.

Intestinal helminths are extremely widespread and highly prevalent infections of humans, particularly in rural and poor urban areas of low and middle-income countries. These parasites have chronic and often insidious effects on human health and child development including abdominal problems, anaemia, stunting and wasting. Certain animals play a fundamental role in the transmission of many intestinal helminths to humans. However, the contribution of zoonotic transmission to the overall burden of human intestinal helminth infection and the relative importance of different animal reservoirs remains incomplete. Moreover, control programmes and transmission models for intestinal helminths often do not consider the role of zoonotic reservoirs of infection. Such reservoirs will become increasingly important as control is scaled up and there is a move towards interruption and even elimination of parasite transmission. With a focus on southeast Asia, and the Philippines in particular, this review summarises the major zoonotic intestinal helminths, risk factors for infection and highlights knowledge gaps related to their epidemiology and transmission. Various methodologies are discussed, including parasite genomics, mathematical modelling and socio-economic analysis, that could be employed to improve understanding of intestinal helminth spread, reservoir attribution and the burden associated with infection, as well as assess effectiveness of interventions. For sustainable control and ultimately elimination of intestinal helminths, there is a need to move beyond scheduled mass deworming and to consider animal and environmental reservoirs. A One Health approach to control of intestinal helminths is proposed, integrating interventions targeting humans, animals and the environment, including improved access to water, hygiene and sanitation. This will require coordination and collaboration across different sectors to achieve best health outcomes for all.

Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis : Analysis of a spatially nonlocal model.

yme disease is transmitted via blacklegged ticks, the spatial spread of which is believed to be primarily via transport on white-tailed deer. In this paper, we develop a mathematical model to describe the spatial spread of blacklegged ticks due to deer dispersal. The model turns out to be a system of differential equations with a spatially non-local term accounting for the phenomenon that a questing female adult tick that attaches to a deer at one location may later drop to the ground, fully fed, at another location having been transported by the deer. We first justify the well-posedness of the model and analyze the stability of its steady states. We then explore the existence of traveling wave fronts connecting the extinction equilibrium with the positive equilibrium for the system. We derive an algebraic equation that determines a critical value c* which is at least a lower bound for the wave speed in the sense that, if c

Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus.

Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number [Formula: see text] is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.

A Mathematical Model for Biocontrol of the Invasive Weed Fallopia japonica.

We propose a mathematical model for biocontrol of the invasive weed Fallopia japonica using one of its co-evolved natural enemies, the Japanese sap-sucking psyllid Aphalara itadori. This insect sucks the sap from the stems of the plant thereby weakening it. Its diet is highly specific to F. japonica. We consider a single isolated knotweed stand, the plant's size being described by time-dependent variables for total stem and rhizome biomass. It is the larvae of A. itadori that damage the plant most, so the insect population is described in terms of variables for the numbers of larvae and adults, using a stage-structured modelling approach. The dynamics of the model depends mainly on a parameter h, which measures how long it takes for an insect to handle (digest) one unit of F. japonica stem biomass. If h is too large, then the model does not have a positive equilibrium and the plant biomass and insect numbers both grow together without bound, though at a lower rate than if the insects were absent. If h is sufficiently small, then the model possesses a positive equilibrium which appears to be locally stable. The results based on our model imply that satisfactory long-term control of the knotweed F. japonica using the insect A. itadori is only possible if the insect is able to consume and digest knotweed biomass sufficiently quickly; if it cannot, then the insect can only slow down the growth which is still unbounded.

Modelling the dynamics of bluetongue disease and the effect of seasonality.

We present mathematical models for the midge-borne disease bluetongue, with cattle and sheep as hosts. The models take the form of delay differential equations and incorporate the incubation time of bluetongue in cattle, sheep and midges, and also the larval developmental time of midges. Recovery in cattle and sheep is also included. Both an autonomous and a periodic model are considered, to take account of seasonality. For both models we present conditions for the disease-free state to be linearly stable, and a detailed interpretation of those conditions. The results of simulations are also presented. Important findings include the need for prompt diagnosis of latent infection and appropriate action before the animal turns infectious, and the need for measures that reduce insect bites.

Delayed action insecticides and their role in mosquito and malaria control.

There is considerable interest in the management of insecticide resistance in mosquitoes. One possible approach to slowing down the evolution of resistance is to use late-life-acting (LLA) insecticides that selectively kill only the old mosquitoes that transmit malaria, thereby reducing selection pressure favoring resistance. In this paper we consider an age-structured compartmental model for malaria with two mosquito strains that differ in resistance to insecticide, using an SEI approach to model malaria in the mosquitoes and thereby incorporating the parasite developmental times for the two strains. The human population is modeled using an SEI approach. We consider both conventional insecticides that target all adult mosquitoes, and LLA insecticides that target only old mosquitoes. According to linearised theory the potency of the insecticide affects mainly the speed of evolution of resistance. Mutations that confer resistance can also affect other parameters such as mean adult life span and parasite developmental time. For both conventional and LLA insecticides the stability of the malaria-free equilibrium, with only the resistant mosquito strain present, depends mainly on these other parameters. This suggests that the main long term role of an insecticide could be to induce genetic changes that have a desirable effect on a vital parameter such as adult life span. However, when this equilibrium is unstable, numerical simulations suggest that a potent LLA insecticide can slow down the spread of malaria in humans but that the timing of its action is very important.

A non-local evolution equation model of cell-cell adhesion in higher dimensional space.

A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.

Modeling the dynamics of woody plant-herbivore interactions with age-dependent toxicity.

In this paper we study the effects that woody plant chemical defenses may have on interactions between boreal hares that in winter feed almost entirely on twigs. We focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by hares is much higher than their intake of the biomass of the younger segments of twigs. This age-dependent toxicity of twig segments is modeled using age-structured model equations which are reduced to a system of delay differential equations involving multiple delays in the woody plant-hare dynamics. A novel aspect of the modeling was that it had to account for mortality of non-consumed younger twig segment biomass when older twig biomass was bitten off and consumed. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for the global stability of this equilibrium. Numerical simulations confirmed the analytical results and demonstrated the existence of limit cycles over ranges of parameters reasonable for hares browsing on woody vegetation in boreal ecosystems. This showed that age dependence in plant chemical defenses has the capacity to cause hare-plant population cycles, a new result.

A delay equation model for oviposition habitat selection by mosquitoes.

We propose a patch type model for mosquitoes that have aquatic larvae inhabiting ponds. Partial differential equations (PDEs) model the larvae on each of several disconnected patches representing the ponds, with conditions varying in each patch, coupled via the adults in the air. From the PDEs a scalar delay differential equation, with multiple delays, for the total adult mosquito population is derived. The various delays represent the larval development times in the patches. The coefficients contain all the relevant information about the sizes and geometry of the individual patches inhabited by the larvae, the boundary conditions applicable to those patches and the diffusivity of the larvae in each patch. For patches of general shapes and sizes, and without the need to specify the criteria by which an adult mosquito selects an oviposition patch, the modern theory of monotone dynamical systems and persistence theory enables a complete determination of the conditions for the mosquito population to go extinct or to persist. More detailed biological insights are obtained for the case when the patches are squares of various sizes, which allows a detailed discussion of the effects of scale, and for two particular criteria by which mosquitoes might select patches for oviposition, being (i) selection based solely on patch area, and (ii) selection based both on area and expected larval survival probability for each patch. In some parameter regimes, counterintuitive phenomena are predicted.

Perverse consequences of infrequently culling a pest.

There are potentially many situations in which creatures will be subject to infrequent but regular culling. In terms of controlling crop pests, some farmers may only be able to afford to apply pesticides occasionally. Alternatively, pesticides may be applied only occasionally to limit their unwelcome side effects, which include pesticide resistance, chemical poisoning of agricultural workers, and environmental degradation. In terms of conservation, some species (such as the red deer in the UK) may be culled occasionally to maintain balances within their ecosystem. However, in this paper we discover, as the culmination of an exploration of adult-stage culling of a creature with juvenile and adult life stages, that, in certain circumstances, regular but infrequent culling will, perversely, increase the average population of the creature.

Dynamics of a delay differential equation model of hepatitis B virus infection.

We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.

Eradicating vector-borne diseases via age-structured culling.

We derive appropriate mathematical models to assess the effectiveness of culling as a tool to eradicate vector-borne diseases. The model, focused on the culling strategies determined by the stages during the development of the vector, becomes either a system of autonomous delay differential equations with impulses (in the case where the adult vector is subject to culling) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where only the immature vector is subject to culling). Sufficient conditions are derived to ensure eradication of the disease, and simulations are provided to compare the effectiveness of larvicides and insecticide sprays for the control of West Nile virus. We show that eradication of vector-borne diseases is possible by culling the vector at either the immature or the mature phase, even though the size of the vector is oscillating and above a certain level.

Two-species competition with high dispersal: the winning strategy.

This paper is motivated by the following simple question: how does diffusion affect the competition outcomes of two competing species that are identical in all respects other than their strategies on how they spatially distribute their birth rates. This may provide us with insights into how species learn to compete in a relatively stable setting, which in turn may point out species evolution directions. To this end, we formulate some extremely simple two-species competition models that have either continuous or discrete diffusion mechanisms. Our analytical work on these models collectively and strongly suggests the following in a fast diffusion environment: where different species have the same birth rates on average, those that do well are those that have greater spatial variation in their birth rates. We hypothesize that this may be a possible explanation for the evolution of grouping behavior in many species. Our findings are confirmed by extensive numerical simulation work on the models.

A stage structured predator-prey model and its dependence on maturation delay and death rate.

Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.