Scott Greenhalgh

Impact of Schistosoma mansoni on Malaria Transmission in Sub-Saharan Africa

Background Sub-Saharan Africa harbors the majority of the global burden of malaria and schistosomiasis infections. The co-endemicity of these two tropical diseases has prompted investigation into the mechanisms of coinfection, particularly the competing immunological responses associated with each disease. Epidemiological studies have shown that infection with Schistosoma mansoni is associated with a greater malaria incidence among school-age children. Methodology We developed a co-epidemic model of malaria and S. mansoni transmission dynamics which takes into account key epidemiological interaction between the two diseases in terms of elevated malaria incidence among individuals with S. mansoni high egg output. The model was parameterized for S. mansoni high-risk endemic communities, using epidemiological and clinical data of the interaction between S. mansoni and malaria among children in sub-Saharan Africa. We evaluated the potential impact of the S. mansoni–malaria interaction and mass treatment of schistosomiasis on malaria prevalence in co-endemic communities. Principal Findings Our results suggest that in the absence of mass drug administration of praziquantel, the interaction between S. mansoni and malaria may reduce the effectiveness of malaria treatment for curtailing malaria transmission, in S. mansoni high-risk endemic communities. However, when malaria treatment is used in combination with praziquantel, mass praziquantel administration may increase the effectiveness of malaria control intervention strategy for reducing malaria prevalence in malaria- S. mansoni co-endemic communities. Conclusions/Significance Schistosomiasis treatment and control programmes in regions where S. mansoni and malaria are highly prevalent may have indirect benefits on reducing malaria transmission as a result of disease interactions. In particular, mass praziquantel administration may not only have the direct benefit of reducing schistosomiasis infection, it may also reduce malaria transmission and disease burden.

The epidemiological impact of HIV antiretroviral therapy on malaria in children

Objective:The objective of this study is to determine the epidemiological effectiveness of a first-line antiretroviral regimen with HIV protease inhibitor for preventing recurrent malaria in children under the range of HIV prevalence levels and malaria transmission intensities encountered in sub-Saharan Africa. Design:A dynamic model of malaria transmission was developed using clinical data on the protease inhibitor extended posttreatment prophylactic effect of the antimalarial treatment, artemether-lumefantrine, in addition to parameter estimates from the literature. Methods:To evaluate the benefits of HIV protease inhibitors on the health burden of recurrent malaria among children, we constructed a dynamic model of malaria transmission to both HIV-positive and HIV-negative children, parameterized by data from a recent clinical trial. The model was then evaluated under varying malaria transmission and HIV prevalence settings to determine the health benefits of HIV protease inhibitors in the context of artemether-lumefantrine treatment of malaria in children. Results:Comparing scenarios of low, intermediate and high newborn HIV prevalence, in a range of malaria transmission settings, our dynamic model predicts that artemether-lumefantrine with HIV protease inhibitor based regimens prevents 0.03–0.10, 5.2–13.0 and 25.5–65.8 annual incidences of malaria per 1000 children, respectively. In addition, HIV protease inhibitors save 0.002–0.006, 0.22–0.8, 1.04–4.3 disability-adjusted life-years per 1000 children annually. Considering only HIV-infected children, HIV protease inhibitors avert between 278 and 1043 annual incidences of malaria per 1000 children. Conclusion:The use of HIV protease inhibitor based regimens as first-line antiretroviral therapy for HIV is an effective measure for reducing recurrent malaria among HIV-infected children in areas where HIV and malaria are coendemic, and artemether-lumefantrine is a first-line antimalarial.

Disease elimination and re-emergence in differential-equation models☆

Traditional differential equation models of disease transmission are often used to predict disease trajectories and evaluate the effectiveness of alternative intervention strategies. However, such models cannot account explicitly for probabilistic events, such as those that dominate dynamics when disease prevalence is low during the elimination and re-emergence phases of an outbreak. To account for the dynamics at low prevalence, i.e. the elimination and risk of disease re-emergence, without the added analytical and computational complexity of a stochastic model, we develop a novel application of control theory. We apply our approach to analyze historical data of measles elimination and re-emergence in Iceland from 1923 to 1938, predicting the temporal trajectory of local measles elimination and re-emerge as a result of disease migration from Copenhagen, Denmark.

Time-varying and state-dependent recovery rates in epidemiological models

Differential equation models of infectious disease have undergone many theoretical extensions that are invaluable for the evaluation of disease spread. For instance, while one traditionally uses a bilinear term to describe the incidence rate of infection, physically more realistic generalizations exist to account for effects such as the saturation of infection. However, such theoretical extensions of recovery rates in differential equation models have only started to be developed. This is despite the fact that a constant rate often does not provide a good description of the dynamics of recovery and that the recovery rate is arguably as important as the incidence rate in governing the dynamics of a system. We provide a first-principles derivation of state-dependent and time-varying recovery rates in differential equation models of infectious disease. Through this derivation, we demonstrate how to obtain time-varying and state-dependent recovery rates based on the family of Pearson distributions and a power-law distribution, respectively. For recovery rates based on the family of Pearson distributions, we show that uncertainty in skewness, in comparison to other statistical moments, is at least two times more impactful on the sensitivity of predicting an epidemics peak. In addition, using recovery rates based on a power-law distribution, we provide a procedure to obtain state-dependent recovery rates. For such state-dependent rates, we derive a natural connection between recovery rate parameters with the mean and standard deviation of a power-law distribution, illustrating the impact that standard deviation has on the shape of an epidemic wave.

Managing Marek's disease in the egg industry

The industrialization of farming has had an enormous impact. To most, this impact is viewed solely in the context of productivity, but the denser living conditions and shorter rearing periods of industrial livestock farms provide pathogens with an ideal opportunity to spread and evolve. For example, the industrialization of poultry farms drove the Marek’s disease virus (MDV) to evolve from causing a mild paralytic syndrome to causing a highly contagious, globally prevalent, disease that can have up to a 100% mortality rate. Fortunately, the economic catastrophe that would occur from MDV evolution has been prevented through widespread use of live imperfect vaccines that limit disease symptoms, but fail to prevent transmission. Unfortunately, the continued rollout of such imperfect vaccines is steering the evolution of MDV towards an even greater virulence and an ability to evade vaccine protection. Thus, there is a need to investigate alternative economically viable control measures for their ability to inhibit MDV spread and evolution. In what follows we examine the economic viability of standard husbandry practices for their ability to inhibit the spread of both virulent MDV and very virulent MDV throughout an industrialized egg farm. To do this, we parameterized a dynamic MDV transmission model and calculate the loss in egg production due to disease. We find that the MDV strain as well as the cohort duration had the greatest influence on disease burden and hence egg production. Additionally, we find that the standard husbandry practice involving conventional cages, often referred to as “battery cages”, results in the least per capita loss in egg production due to MDV infection when compared to alternative enriched or aviary (free-run) systems for virulent MDV, but not very virulent MDV, in which case the Aviary system performs the best. These results highlight an important cost that managers will face when implementing new hen husbandry practices.

Non-equilibrium Solutions of Dynamic Networks: A Hybrid System Approach

Many dynamic networks can be analyzed through the framework of equilibrium problems. While traditionally, the study of equilibrium problems is solely concerned with obtaining or approximating equilibrium solutions, the study of equilibrium problems not in equilibrium provides valuable information into dynamic network behavior. One approach to study such non-equilibrium solutions stems from a connection between equilibrium problems and a class of parametrized projected differential equations. However, there is a drawback of this approach: the requirement of observing distributions of demands and costs. To address this problem we develop a hybrid system framework to model non-equilibrium solutions of dynamic networks, which only requires point observations. We demonstrate stability properties of the hybrid system framework and illustrate the novelty of our approach with a dynamic traffic network example.

Modelling the impact of antimalarial quality on the transmission of sulfadoxine-pyrimethamine resistance in Plasmodium falciparum

Background The use of poor quality antimalarial medicines, including the use of non-recommended medicines for treatment such as sulfadoxine-pyrimethamine (SP) monotherapy, undermines malaria control and elimination efforts. Furthermore, the use of subtherapeutic doses of the active ingredient(s) can theoretically promote the emergence and transmission of drug resistant parasites. Methods We developed a deterministic compartmental model to quantify the impact of antimalarial medicine quality on the transmission of SP resistance, and validated it using sensitivity analysis and a comparison with data from Kenya collected in 2006. We modelled human and mosquito population dynamics, incorporating two Plasmodium falciparum subtypes (SP-sensitive and SP-resistant) and both poor quality and good quality (artemether-lumefantrine) antimalarial use. Findings The model predicted that an increase in human malaria cases, and among these, an increase in the proportion of SP-resistant infections, resulted from an increase in poor quality SP antimalarial use, whether it was full- or half-dose SP monotherapy. Interpretation Our findings suggest that an increase in poor quality antimalarial use predicts an increase in the transmission of resistance. This highlights the need for stricter control and regulation on the availability and use of poor quality antimalarial medicines, in order to offer safe and effective treatments, and work towards the eradication of malaria.

Evolution Solutions of Equilibrium Problems: A Computational Approach

This paper proposes a computational method to describe evolution solutions of known classes of time-dependent equilibrium problems (such as time-dependent traffic network, market equilibrium or oligopoly problems, and dynamic noncooperative games). Equilibrium solutions for these classes have been studied extensively from both a theoretical (regularity, stability behaviour) and a computational point of view. In this paper we highlight a method to further study the solution set of such problems from a dynamical systems perspective, namely we study their behaviour when they are not in an (market, traffic, financial, etc.) equilibrium state. To this end, we define what is meant by an evolution solution for a time-dependent equilibrium problem and we introduce a computational method for tracking and visualizing evolution solutions using a projected dynamical system defined on a carefully chosen L2-space. We strengthen our results with various examples.

A Dynamic Pricing Game in a Model of New Product Adoption with Social Influence

We examine a pricing game between firms that produce differentiated products and in which consumer preferences evolve in response to the market shares of the available products. One of the products is new and a subset of consumers (early adopters) have a relatively strong preference for it, while the remaining consumers are influenced by the relative market shares of the two products, being drawn to the product with the higher market share. We use a system of PDEs to specify the evolution of the preferences for the alternative goods. This system is nonlinear due to the influence of existing consumption choice on the distribution of preferences. The pricing game allows firms to react to the changing distribution of consumer preference. We find that allowing for the evolution of consumer preference in this way results in interesting dynamics for prices. In particular, price paths can be non-monotonic over time.

Dynamics of Equilibrium Problems: A Hybrid Systems Approach

This paper relates variational inequalities, and hybrid dynamical systems to describe the evolution of an equilibrium problem over a finite time interval. To describe such evolution, we define a hybrid dynamical system with a “switch and jump” mechanism between continuous dynamics described by a projected system. This hybrid system is used to track the evolution of the underlying applied problem in a disequilibrium state. Its solutions can be computed with a projection‐like method. We apply our results to track the evolution of population groups’ strategies playing a noncooperative vaccinating game.