Showing papers by "Robert J. Smith published in 2016"

Optimal control analysis of malaria-schistosomiasis co-infection dynamics.

Abstract: This paper presents a mathematical model for malaria-schistosom-iasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.

An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza.

Abstract: Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states; the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.

A mathematical model of ebola virus disease: using sensitivity analysis to determine effective intervention targets

Abstract: Mathematical models provide a useful framework to investigate real-world problems. They can be used in the context of disease dynamics to study how a disease will spread and how we can stop or prevent an outbreak. In December of 2013, an outbreak of Ebola began in the West African country of Guinea and later spread to Sierra Leone and Liberia. Health Organisations like the US Centers for Disease Control and the World Health Organization were tasked with providing aid to end the outbreak. We create an SEIR compartmental model of Ebola with a fifth compartment for the infectious deceased to model the dynamics of an Ebola outbreak in a village of a thousand people. We analyse the disease-free equilibrium of the model and formulate an equation for the eradication threshold R0. Sensitivity analyses points us in the direction of the transmission probability and the contact rate with infectious individuals as targets for intervention. We model the effect that vaccination and quarantine, together and separately, have on the outcome of the Ebola epidemic. We find that quarantine is a very effective intervention, but when combined with vaccination it can theoretically lead to eradication of the disease.

Mathematical Modelling of Enfuvirtide and Protease Inhibitors as Combination Therapy for HIV

Abstract: Abstract Enfuvirtide (formerly T20) is an injectable fusion inhibitor that has established effective antiretroviral activity and excellent tolerability in extensively pretreated patients. This fusion inhibitor does not affect the metabolism of other co-administrated drugs for metabolic drug interactions involving enfuvirtide. Few mathematical models have considered co-administration of antiretroviral drugs. We develop a mathematical model to study the effect of enfuvirtide upon this process in combination with protease inhibitors (PIs) using impulsive differential equations. We divide the T cells into several classes to describe the drug activity. Analytical results show that a combination of enfuvirtide and PIs gives a better outcome than single drug activity; furthermore, use of enfuvirtide clearly outranks PIs if only one class of drugs were to be used. We determine the threshold value for the dosage and dosing intervals to ensure the stability of the disease-free state and illustrate our results with numerical simulations. We recommend that use of enfuvirtide, in combination with PIs, be expanded beyond salvage therapy.

Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?

Abstract: There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The impulse is triggered either due to periodic spraying or when a critical number of malaria cases are detected. For small mutation rates, the mosquito-only submodel exhibits either a single mutant-only equilibrium, a mutant-only equilibrium and a single coexistence equilibrium, or a mutant-only equilibrium and a pair of coexistence equilibria. Bistability is a likely outcome, while the effect of impulses is to introduce a saddle-node bifurcation, resulting in persistence of malaria in the form of impulsive periodic orbits. If certain parameters are small, triggering the insecticide based on number of malaria cases is asymptotically equivalent to spraying periodically.

Multiseason transmission for Rift Valley fever in North America

Abstract: Rift Valley fever is a vector-borne disease, primarly found in West Africa, that is transmitted to humans and domestic livestock. Its similarities to the West Nile virus suggest that establishment in the developed world may be possible. Rift Valley fever has the potential to invade North America, where seasons play a role in disease persistence. The values for the basic reproductive number show that, in order to eradicate the disease, the survival time of mosquitoes must decrease below 8.67 days. Mechanisms such as aggressive spraying that decreases the mosquito population can contain an outbreak. Otherwise, Rift Valley fever is likely to establish itself as a recurring seasonal outbreak. Rift Valley fever poses a potential threat to North America that would require aggressive interventions in order to prevent a recurring seasonal outbreak.

Population modelling by examples ii

Abstract: Population modelling spans many domains and techniques, and new technologies offer cutting-edge opportunities to a growing field. The population modelling working group has been recently active in coordination amongst different population modellers of different fields. One activity is mapping the population modelling domain by examples of work. This is the second collaborative paper by group members. This paper includes new examples and new authors in an attempt to define the field. Some analysis and discussion is provided in view of the existing examples.

On the Co-infection of Malaria and Schistosomiasis

Abstract: Mathematical models for co-infection of diseases (that is, the simultaneous infection of an individual by multiple diseases) are sorely lacking in the literature. Here we present a mathematical model for the co-infection of malaria and schistosomiasis. We derive reproduction numbers for malaria and schistosomiasis independently, then combine these to determine the effects of disease interactions. Sensitivity indices show that malaria infection may be associated with an increased rate of schistosomiasis infection. However, schistosomiasis infection is not associated with an increased rate of malaria infection. Therefore, whenever there is co-infection of malaria and schistosomiasis in the community, our model suggests that control measures for each disease should be administered concurrently for effective control.

A mathematical model of a theoretical sleeping sickness vaccine

Abstract: Human African sleeping sickness is found throughout sub-Saharan Africa. It affects up to 70,000 individuals per year, primarily the poor. Existing treatments are limited, costly, and often toxic. Recent evidence suggests that a vaccine may be viable. Potential vaccines against Rhodesian sleeping sickness may be imperfect, may only be delivered to some proportion of the population, may wane over time, and may not always mount an immunogenic response in the individual receiving it. The potential effects of such a vaccine are addressed and compared to vector control. The basic reproductive ratio for both unvaccinated and vaccinated individuals is derived. The fitness ratio is used to show that vaccines that grant longer life must be accompanied by a corresponding reduction in transmissibility. A sensitivity analysis shows that control of tsetse flies through insecticide is superior to an idealized vaccine. Such a vaccine is unlikely to eradicate the disease, even if delivered to 100% of the populatio...

Applications of mathematical modeling in managing the spread of chronic wasting disease (CWD) in wild deer under alternative harvesting scenarios.

Abstract: The application of a recently developed mathematical model for predicting the spread of chronic wasting disease (CWD) in wild deer was assessed under different scenarios where harvesting is employed in disease management. A process-based mathematical model for CWD transmission in wild deer populations was recently developed and parameterized by Al-arydah et al. (2011) to provide a scientific basis for understanding the factors that affect spread of CWD and evaluate concomitant disease-control strategies. The impact of gender on CWD transmission was shown to have a significant influence on the spread of the disease in the wild. Our model demonstrates a range of harvesting rates in which CWD is controlled and deer populations survive. However, if harvesting rates are too low, the disease remains endemic for decades. Conversely, the Canadian deer population is eradicated if harvesting rates are excessive. Future investigation includes building the model to assess the spread of CWD under different disease-management scenarios.