Mass campaigns with antimalarial drugs: a modelling comparison of artemether-lumefantrine and DHA-piperaquine with and without primaquine as tools for malaria control and elimination

Antimalarial drugs are a powerful tool for malaria control and elimination. Artemisinin-based combination therapies (ACTs) can reduce transmission when widely distributed in a campaign setting. Modelling mass antimalarial campaigns can elucidate how to most effectively deploy drug-based interventions and quantitatively compare the effects of cure, prophylaxis, and transmission-blocking in suppressing parasite prevalence. A previously established agent-based model that includes innate and adaptive immunity was used to simulate malaria infections and transmission. Pharmacokinetics of artemether, lumefantrine, dihydroartemisinin, piperaquine, and primaquine were modelled with a double-exponential distribution-elimination model including weight-dependent parameters and age-dependent dosing. Drug killing of asexual parasites and gametocytes was calibrated to clinical data. Mass distribution of ACTs and primaquine was simulated with seasonal mosquito dynamics at a range of transmission intensities. A single mass campaign with antimalarial drugs is insufficient to permanently reduce malaria prevalence when transmission is high. Current diagnostics are insufficiently sensitive to accurately identify asymptomatic infections, and mass-screen-and-treat campaigns are much less efficacious than mass drug administrations. Improving campaign coverage leads to decreased prevalence one month after the end of the campaign, while increasing compliance lengthens the duration of protection against reinfection. Use of a long-lasting prophylactic as part of a mass drug administration regimen confers the most benefit under conditions of high transmission and moderately high coverage. Addition of primaquine can reduce prevalence but exerts its largest effect when coupled with a long-lasting prophylactic.Comment: 14 pages, 5 figure

Metastability and low lying spectra in reversible Markov chains

We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space \G_N such that (i) this set is reached from any point x\in \G_N without return to x with probability at least $b_N$, while (ii) for any two point x,y in the metastable set, the probability $T^{-1}_{x,y}$ to reach y from x without return to x is smaller than $a_N^{-1}\ll b_N$. Under some additional non-degeneracy assumption, we show that in such a situation: \item{(i)} To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. \item{(ii)} To each metastable point corresponds one simple eigenvalue of $1-P_N$ which is essentially equal to the inverse mean exit time from this state. The corresponding eigenfunctions are close to the indicator function of the support of the metastable state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution.Comment: 44pp, AMSTe

Metastability in stochastic dynamics of disordered mean-field models

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of ``admissible transitions''. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.Comment: 73pp, AMSTE

Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

Optimal population-level infection detection strategies for malaria control and elimination in a spatial model of malaria transmission

Mass campaigns with antimalarial drugs are potentially a powerful tool for local elimination of malaria, yet current diagnostic technologies are insufficiently sensitive to identify all individuals who harbor infections. At the same time, overtreatment of uninfected individuals increases the risk of accelerating emergence of drug resistance and losing community acceptance. Local heterogeneity in transmission intensity may allow campaign strategies that respond to index cases to successfully target subpatent infections while simultaneously limiting overtreatment. While selective targeting of hotspots of transmission has been proposed as a strategy for malaria control, such targeting has not been tested in the context of malaria elimination. Using household locations, demographics, and prevalence data from a survey of four health facility catchment areas in southern Zambia and an agent-based model of malaria transmission and immunity acquisition, a transmission intensity was fit to each household based on neighborhood age-dependent malaria prevalence. A set of individual infection trajectories was constructed for every household in each catchment area, accounting for heterogeneous exposure and immunity. Various campaign strategies (mass drug administration, mass screen and treat, focal mass drug administration, snowball reactive case detection, pooled sampling, and a hypothetical serological diagnostic) were simulated and evaluated for performance at finding infections, minimizing overtreatment, reducing clinical case counts, and interrupting transmission. For malaria control, presumptive treatment leads to substantial overtreatment without additional morbidity reduction under all but the highest transmission conditions. Selective targeting of hotspots with drug campaigns is an ineffective tool for elimination due to limited sensitivity of available field diagnostics

Helly-Type Theorems in Property Testing

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into $k$ clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object $G$. In this paper, as an application of Helly's theorem, by taking a constant size sample from $S$, we present a testing algorithm for $(k,G)$-clustering, i.e., to distinguish between two cases: when $S$ is $(k,G)$-clusterable, and when it is $\epsilon$-far from being $(k,G)$-clusterable. A set $S$ is $\epsilon$-far $(0<\epsilon\leq1)$ from being $(k,G)$-clusterable if at least $\epsilon n$ points need to be removed from $S$ to make it $(k,G)$-clusterable. We solve this problem for $k=1$ and when $G$ is a symmetric convex object. For $k>1$, we solve a weaker version of this problem. Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Malaria elimination campaigns in the Lake Kariba region of Zambia: a spatial dynamical model

Background As more regions approach malaria elimination, understanding how different interventions interact to reduce transmission becomes critical. The Lake Kariba area of Southern Province, Zambia, is part of a multi-country elimination effort and presents a particular challenge as it is an interconnected region of variable transmission intensities. Methods In 2012-13, six rounds of mass-screen-and-treat drug campaigns were carried out in the Lake Kariba region. A spatial dynamical model of malaria transmission in the Lake Kariba area, with transmission and climate modeled at the village scale, was calibrated to the 2012-13 prevalence survey data, with case management rates, insecticide-treated net usage, and drug campaign coverage informed by surveillance. The model was used to simulate the effect of various interventions implemented in 2014-22 on reducing regional transmission, achieving elimination by 2022, and maintaining elimination through 2028. Findings The model captured the spatio-temporal trends of decline and rebound in malaria prevalence in 2012-13 at the village scale. Simulations predicted that elimination required repeated mass drug administrations coupled with simultaneous increase in net usage. Drug campaigns targeted only at high-burden areas were as successful as campaigns covering the entire region. Interpretation Elimination in the Lake Kariba region is possible through coordinating mass drug campaigns with high-coverage vector control. Targeting regional hotspots is a viable alternative to global campaigns when human migration within an interconnected area is responsible for maintaining transmission in low-burden areas

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Lines pinning lines

A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.Comment: 27 pages, 10 figure