Modelling the effect of temperature on the seasonal population dynamics of temperate mosquitoes.

Mosquito-borne diseases cause substantial mortality and morbidity worldwide. These impacts are widely predicted to increase as temperatures warm and extreme precipitation events become more frequent, since mosquito biology and disease ecology are strongly linked to environmental conditions. However, direct evidence linking environmental change to changes in mosquito-borne disease is rare, and the ecological mechanisms that may underpin such changes are poorly understood. Environmental drivers, such as temperature, can have non-linear, opposing impacts on the demographic rates of different mosquito life cycle stages. As such, model frameworks that can deal with fluctuations in temperature explicitly are required to predict seasonal mosquito abundance, on which the intensity and persistence of disease transmission under different environmental scenarios depends. We present a novel, temperature-dependent, delay-differential equation model, which incorporates diapause and the differential effects of temperature on the duration and mortality of each life stage and demonstrates the sensitivity of seasonal abundance patterns to inter- and intra-annual changes in temperature. Likely changes in seasonal abundance and exposure to mosquitoes under projected changes in UK temperatures are presented, showing an increase in peak vector abundance with warming that potentially increases the risk of disease outbreaks.

Evolution stabilises the synchronising dynamics of poikilotherm life cycles.

Temperature is the most significant factor controlling developmental timing of most temperate poikilotherms. In the face of climate change, a crucial question is how will poikilothermic organisms evolve when faced with changing thermal environments? In this paper, we integrate models for developmental timing and quantitative genetics. A simple model for determining developmental milestones (emergence times, egg hatch) is introduced, and the general quantitative genetic recursion for the mean value of developmental parameters presented. Evolutionary steps proportional to the difference between current median parameters and parameters currently selected for depend on the fitness, which is assumed to depend on emergence density. Asymptotic states of the joint model are determined, which turn out to be neutrally stable (marginal) fixed points in the developmental model by itself, and an associated stable emergence distribution is also described. An asymptotic convergence analysis is presented for idealized circumstances, indicating basic stability criteria. Numerical studies show that the stability analysis is quite conservative, with basins of attraction to the asymptotic states that are much larger than expected. It is shown that frequency-dependent selection drives oscillatory dynamics and that the asymptotic states balance the asymmetry of the emergence distribution and the fitness function.

Critical interplay between parasite differentiation, host immunity, and antigenic variation in trypanosome infections.

Increasing availability of pathogen genomic data offers new opportunities to understand the fundamental mechanisms of immune evasion and pathogen population dynamics during chronic infection. Motivated by the growing knowledge on the antigenic variation system of the sleeping sickness parasite, the African trypanosome, we introduce a mechanistic framework for modeling within-host infection dynamics. Our analysis focuses first on a single parasitemia peak and then on the dynamics of multiple peaks that rely on stochastic switching between groups of parasite variants. A major feature of trypanosome infections is the interaction between variant-specific host immunity and density-dependent parasite differentiation to transmission life stages. In this study, we investigate how the interplay between these two types of control depends on the modular structure of the parasite antigenic archive. Our model shows that the degree of synchronization in stochastic variant emergence determines the relative dominance of general over specific control within a single peak. A requirement for multiple-peak dynamics is a critical switch rate between blocks of antigenic variants, which implies constraints on variant surface glycoprotein (VSG) archive genetic diversification. Our study illustrates the importance of quantifying the links between parasite genetics and within-host dynamics and provides insights into the evolution of trypanosomes.

How parasitism affects critical patch-size in a host-parasitoid model: application to the forest tent caterpillar.

Habitat structure has broad impacts on many biological systems. In particular, habitat fragmentation can increase the probability of species extinction and on the other hand it can lead to population outbreaks in response to a decline in natural enemies. An extreme consequence of fragmentation is the isolation of small regions of suitable habitat surrounded by a large region of hostile matrix. This scenario can be interpreted as a critical patch-size problem, well studied in a continuous time framework, but relatively new to discrete time models. In this paper we present an integrodifference host-parasitoid model, discrete in time and continuous in space, to study how the critical habitat-size necessary for parasitoid survival changes in response to parasitoid life history traits, such as emergence time. We show that early emerging parasitoids may be able to persist in smaller habitats than late emerging species. The model predicts that these early emerging parasitoids lead to more severe host outbreaks. We hypothesise that promoting efficient late emerging parasitoids may be key in reducing outbreak severity, an approach requiring large continuous regions of suitable habitat. We parameterise the model for the host species of the forest tent caterpillar Malacosoma disstria Hbn., a pest insect for which fragmented landscape increases the severity of outbreaks. This host is known to have several parasitoids, due to paucity of data and as a first step in the modelling we consider a single generic parasitoid. The model findings are related to observations of the forest tent caterpillar offering insight into this host-parasitoid response to habitat structure.

Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach.

Atherosclerosis is a chronic disease which involves the build up of cholesterol and fatty deposits within the arterial wall. This results in the narrowing of the vessel lumen, which eventually restricts blood flow to vital organs such as the heart and lungs. These events may culminate in a heart attack or stroke, the commonest causes of death in the U.K. population. In this paper we study the early stages of atherosclerosis which include the build up of cholesterol within subendothelial cells to form what is known as a fatty streak, the earliest identifiable evidence of atherosclerosis. The deposition of cholesterol is believed to be a consequence of oxidation of circulating cholesterol-rich lipoproteins, in particular low density lipoproteins (LDLs). Via a mathematical model we investigate this process of oxidation within the context of an in vitro framework. We first recreate existing experimental results and then extend the model to investigate phenomenon not studied by current experimental protocols. We find that the model displays hysteresis which reveals some interesting insights into possible in vivo events. Mathematical analysis of this behaviour predicts that vitamin E supplementation is not as beneficial as high density lipoproteins (HDLs) and vitamin C. Furthermore, the scavenging of oxidants by HDL can provide an important first line of defence against LDL oxidation.

The role of nitric oxide in the formation of keloid and hypertrophic lesions.

Keloid and hypertrophic scars are a type of scarring pathology which is characterised by excess collagen deposition produced during the wound healing process. The mechanism by which this occurs is not understood and although hypertrophic scars can regress spontaneously, keloids do not, and currently no effective treatment exists. In this paper we hypothesise that nitric oxide, a free radical molecule synthesised by numerous mammalian cells, is involved in the formation of these scars. We suggest that the excess collagen production in keloid lesions can be attributed to higher than normal levels of nitric oxide, as the free radical is a known stimulus for fibroblast collagen synthesis. Furthermore, we propose that the basal epidermis is a source of this additional nitric oxide and we discuss this in relation to known histological characteristics of keloid and hypertrophic lesions.

Mathematical modelling of nitric oxide activity in wound healing can explain keloid and hypertrophic scarring.

Keloid and hypertrophic lesions are both types of scarring pathologies which arise as a consequence of excess collagen deposition during the wound healing process. The exact mechanism by which this occurs is not understood and currently no effective treatment exists. In this paper, we study the possible role of nitric oxide in excess scar formation. In recent years, the physiological role of this free radical in mammalian tissue has been extensively studied; in particular numerous groups have studied its role in wound healing. We describe a mathematical model which offers a possible explanation for keloid scarring in terms of the presence of higher than normal nitric oxide concentrations related to the fact that nitric oxide stimulates synthesis of collagen by fibroblasts. As a consequence of this, we put forward a suggestion for a treatment strategy involving the surgical excision of the keloid lesion combined with the application of a low-dose nitric oxide inhibitor. In addition, we show that a quasi-steady-state analysis of our model reveals a possible approach to distinguishing between hypertrophic and keloid lesions, a task which has to date proven to be clinically difficult. We also present an extended model which confirms these results in the context of a more complicated and biologically more realistic system. The fuller model demonstrates additional features of keloid and hypertrophic scarring which we were not able to consider in the basic model, and as a consequence further supports our hypothesis that nitric oxide activity could play a key role in keloid scarring.