Optimal Control of Epidemic Models Involving Rabies and West Nile Viruses

This research considers the application of Optimal Control theory to minimize the spread of viral infections in disease models. The population models under consideration are systems of ordinary differential equations and represent epidemics arising due to either rabies or West Nile virus. Optimal control strategies are analyzed using Pontryagin’s Maximum Principle and illustrated based upon computer simulations. The first model describes a population of raccoons and its interaction with the rabies virus, thus dividing the animals into four classes: susceptible, exposed, immune, and recovered (SEIR). The model includes a birth pulse during the spring of the year and an equation reflecting the dynamics of a potential vaccine. The vaccine equation contains a linear control variable representing the rate at which the vaccine is distributed. The goal is to minimize the number of infected raccoons and the cost of vaccine distributed. Due to linearity in the control, there is the possibility of a singular control and the generalized Legendre-Clebsch condition will be satisfied to obtain new necessary conditions for the singular case. A scenario with a limited amount of vaccine is also investigated. The system is modified to include a density-dependent death rate for each of the S, E, I, R classes, and the results of this model are compared with those of the non-density dependent model to determine how the different death rates affect control strategies. The second disease model considered describes the dynamics of mosquito, bird and human populations exposed to the West Nile virus. The mosquito and bird categories will be divided into susceptible and infected classes. In addition to these two groups, humans will also have the potential of entering the exposed, hospitalized and recovered classes. In this model, birth and death rates are assumed to be density-dependent. Two controls are applied with one control representing pesticide efforts to decrease the number of mosquitos and a second control representing prevention and repellant methods. The basic reproduction number is considered to justify the need for control. Approximations of the optimal solutions of the models are obtained using an iterative method. The numerical algorithm, Runge-Kutta of order four, is programmed in Matlab. Graphical results show the appropriate amount of control for various situations

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention

Use of quantitative molecular diagnostic methods to identify causes of diarrhoea in children: a reanalysis of the GEMS case-control study.

BACKGROUND: Diarrhoea is the second leading cause of mortality in children worldwide, but establishing the cause can be complicated by diverse diagnostic approaches and varying test characteristics. We used quantitative molecular diagnostic methods to reassess causes of diarrhoea in the Global Enteric Multicenter Study (GEMS). METHODS: GEMS was a study of moderate to severe diarrhoea in children younger than 5 years in Africa and Asia. We used quantitative real-time PCR (qPCR) to test for 32 enteropathogens in stool samples from cases and matched asymptomatic controls from GEMS, and compared pathogen-specific attributable incidences with those found with the original GEMS microbiological methods, including culture, EIA, and reverse-transcriptase PCR. We calculated revised pathogen-specific burdens of disease and assessed causes in individual children. FINDINGS: We analysed 5304 sample pairs. For most pathogens, incidence was greater with qPCR than with the original methods, particularly for adenovirus 40/41 (around five times), Shigella spp or enteroinvasive Escherichia coli (EIEC) and Campylobactor jejuni o C coli (around two times), and heat-stable enterotoxin-producing E coli ([ST-ETEC] around 1·5 times). The six most attributable pathogens became, in descending order, Shigella spp, rotavirus, adenovirus 40/41, ST-ETEC, Cryptosporidium spp, and Campylobacter spp. Pathogen-attributable diarrhoeal burden was 89·3% (95% CI 83·2-96·0) at the population level, compared with 51·5% (48·0-55·0) in the original GEMS analysis. The top six pathogens accounted for 77·8% (74·6-80·9) of all attributable diarrhoea. With use of model-derived quantitative cutoffs to assess individual diarrhoeal cases, 2254 (42·5%) of 5304 cases had one diarrhoea-associated pathogen detected and 2063 (38·9%) had two or more, with Shigella spp and rotavirus being the pathogens most strongly associated with diarrhoea in children with mixed infections. INTERPRETATION: A quantitative molecular diagnostic approach improved population-level and case-level characterisation of the causes of diarrhoea and indicated a high burden of disease associated with six pathogens, for which targeted treatment should be prioritised. FUNDING: Bill & Melinda Gates Foundation

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

BACKGROUND: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. METHODS: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). FINDINGS: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29-146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0- 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25-1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39-1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65-1·60]; p=0·92). INTERPRETATION: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention. FUNDING: British Heart Foundation

“How Many Earths?” (Semester Unknown) IPRO 332: HowManyEarthsIPRO332MidTermPresentationSp09

The mission of “How Many Earths?” is to educate people on the issues of sustainability and energy needs, concerns, and sources. In doing this we look to expand on work that has been done in previous semesters in addition to developing modules for a wider age base. Previously the modules have been focused on High School and Middle School students; this semester, we look to develop a program for elementary school classrooms in addition to post-high school education.Deliverable

“How Many Earths?” (Semester Unknown) IPRO 332: HowManyEarthsIPRO332PosterSp09

The mission of “How Many Earths?” is to educate people on the issues of sustainability and energy needs, concerns, and sources. In doing this we look to expand on work that has been done in previous semesters in addition to developing modules for a wider age base. Previously the modules have been focused on High School and Middle School students; this semester, we look to develop a program for elementary school classrooms in addition to post-high school education.Deliverable

“How Many Earths?” (Semester Unknown) IPRO 332: HowManyEarthsIPRO332ProjectPlanSp09_redacted

The mission of “How Many Earths?” is to educate people on the issues of sustainability and energy needs, concerns, and sources. In doing this we look to expand on work that has been done in previous semesters in addition to developing modules for a wider age base. Previously the modules have been focused on High School and Middle School students; this semester, we look to develop a program for elementary school classrooms in addition to post-high school education.Deliverable

“How Many Earths?” (Semester Unknown) IPRO 332: HowManyEarthsIPRO332AbstractSp09

The mission of “How Many Earths?” is to educate people on the issues of sustainability and energy needs, concerns, and sources. In doing this we look to expand on work that has been done in previous semesters in addition to developing modules for a wider age base. Previously the modules have been focused on High School and Middle School students; this semester, we look to develop a program for elementary school classrooms in addition to post-high school education.Deliverable