Spatial information allows inference of the prevalence of direct cell-to-cell viral infection

The role of direct cell-to-cell spread in viral infections - where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment - has come to be understood as essential to the dynamics of medically significant viruses like hepatitis C and influenza. Recent work in both the experimental and mathematical modelling literature has attempted to quantify the prevalence of cell-to-cell infection compared to the conventional free virus route using a variety of methods and experimental data. However, estimates are subject to significant uncertainty and moreover rely on data collected by inhibiting one mode of infection by either chemical or physical factors. These methods assume that this inhibition process fully eliminates its target mode of infection while exactly preserving the dynamics of the other. In this work, we provide a framework for estimating the prevalence of cell-to-cell infection from data which is experimentally obtainable without the need for additional interventions, and two standard mathematical models for viral dynamics with the two modes of infection. We provide guidance for the design of relevant experiments and mathematical tools for accurately inferring the prevalence of cell-to-cell infection

On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.Comment: 25 pages, published in Journal of Mathematical Physic

Diagnosis and Antiviral Intervention Strategies for Mitigating an Influenza Epidemic

BACKGROUND: Many countries have amassed antiviral stockpiles for pandemic preparedness. Despite extensive trial data and modelling studies, it remains unclear how to make optimal use of antiviral stockpiles within the constraints of healthcare infrastructure. Modelling studies informed recommendations for liberal antiviral distribution in the pandemic phase, primarily to prevent infection, but failed to account for logistical constraints clearly evident during the 2009 H1N1 outbreaks. Here we identify optimal delivery strategies for antiviral interventions accounting for logistical constraints, and so determine how to improve a strategy's impact. METHODS AND FINDINGS: We extend an existing SEIR model to incorporate finite diagnostic and antiviral distribution capacities. We evaluate the impact of using different diagnostic strategies to decide to whom antivirals are delivered. We then determine what additional capacity is required to achieve optimal impact. We identify the importance of sensitive and specific case ascertainment in the early phase of a pandemic response, when the proportion of false-positive presentations may be high. Once a substantial percentage of ILI presentations are caused by the pandemic strain, identification of cases for treatment on syndromic grounds alone results in a greater potential impact than a laboratory-dependent strategy. Our findings reinforce the need for a decentralised system capable of providing timely prophylaxis. CONCLUSIONS: We address specific real-world issues that must be considered in order to improve pandemic preparedness policy in a practical and methodologically sound way. Provision of antivirals on the scale proposed for an effective response is infeasible using traditional public health outbreak management and contact tracing approaches. The results indicate to change the transmission dynamics of an influenza epidemic with an antiviral intervention, a decentralised system is required for contact identification and prophylaxis delivery, utilising a range of existing services and infrastructure in a "whole of society" response

A Multiscale Mathematical Model of Plasmodium Vivax Transmission

Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as ‘hypnozoites’, they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as ‘relapses’. As around 79–96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels

Excess Risk of Maternal Death from Sickle Cell Disease in Jamaica: 1998–2007

Background: Decreases in direct maternal deaths in Jamaica have been negated by growing indirect deaths. With sickle cell disease (SCD) a consistent underlying cause, we describe the epidemiology of maternal deaths in this population. Methods: Demographic, service delivery and cause specific mortality rates were compared among women with (n = 42) and without SCD (n = 376), and between SCD women who died in 1998–2002 and 2003–7. Results: Women with SCD had fewer viable pregnancies (p: 0.02) despite greater access to high risk antenatal care (p: 0.001), and more often died in an intensive care unit (p: 0.002). In the most recent period (2003–7) SCD women achieved more pregnancies (median 2 vs. 3; p: 0.009), made more antenatal visits (mean 3.3 vs. 7.3; p: 0.01) and were more often admitted antenatally (p:,0.0001). The maternal mortality ratio for SCD decedents was 7–11 times higher than the general population, with 41 % of deaths attributable to their disorder. Cause specific mortality was higher for cardiovascular complications, gestational hypertension and haemorrhage. Respiratory failure was the leading immediate cause of death. Conclusions: Women with SCD experience a significant excess risk of dying in pregnancy and childbirth [MMR: (SCD) 719/ 100,000, (non SCD) 78/100,000]. MDG5 cannot be realised without improving care for women with SCD. Tertiary services (e.g. ventilator support) are needed at regional centres to improve outcomes in this and other high risk populations. Universal SCD screening in pregnancy in populations of African and Mediterranean descent is needed as are guidelines fo