A class of pairwise models for epidemic dynamics on weighted networks

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations

Impact of constrained rewiring on network structure and node dynamics

In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic.We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network’s initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence

Fast variables determine the epidemic threshold in the pairwise model with an improved closure

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks exhibiting degree heterogeneity, directed and/or weighted links and clustering. However, extra features of the disease dynamics or of the network lead to an increase in system size and analytical tractability becomes problematic. Various `closures' can be used to keep the system tractable. Focusing on SIR epidemics on regular but clustered networks, we show that even for the most complex closure we can determine the epidemic threshold as an asymptotic expansion in terms of the clustering coefficient.We do this by exploiting the presence of a system of fast variables, specified by the correlation structure of the epidemic, whose steady state determines the epidemic threshold. While we do not find the steady state analytically, we create an elegant asymptotic expansion of it. We validate this new threshold by comparing it to the numerical solution of the full system and find excellent agreement over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. The technique carries over to pairwise models with other closures [1] and we note that the epidemic threshold will be model dependent. This emphasises the importance of model choice when dealing with realistic outbreaks

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Evaluation of trends in hospital antimicrobial use in the Lao PDR using repeated point-prevalence surveys-evidence to improve treatment guideline use

Background Antimicrobial use (AMU) is a key driver of antimicrobial resistance (AMR). There are few data on AMU, to inform optimizing antibiotic stewardship, in the Lao PDR (Laos). Methods Point prevalence surveys (PPS) of AMU were conducted at four-month intervals in six general hospitals across Laos from 2017 to 2020, using modified Global-PPS data collection tools. The surveys focused on AMU amongst hospitalized inpatients. Findings The overall prevalence of inpatient AMU was 71% (4,377/6,188), varying by hospital and survey round from 50·4% (135/268) to 88·4% (61/69). Of 4,377 patients, 44% received >one antimicrobial. The total number of prescriptions assessed was 6,555. Ceftriaxone was the most commonly used (39·6%) antimicrobial, followed by metronidazole (17%) and gentamicin (10%). Pneumonia was the most common diagnosis among those prescribed antimicrobials in both children aged ≤5 years (29% among aged ≤1 year and 27% among aged >1 to ≤5years) and adults aged ≥15 years at 9%. The percentage of antimicrobial use compliant with local treatment guidelines was 26%; inappropriate use was mainly found for surgical prophylaxis (99%). Adult patients received ACCESS group antimicrobials less commonly than children (47% vs 63%, p-value<0·0001). Most WATCH group prescriptions (99%) were without a microbiological indication. Interpretation AMU among hospitalized patients in Laos is high with frequent inappropriate use of antimicrobials, especially as surgical prophylaxis. Continued monitoring and enhanced antimicrobial stewardship interventions are needed in Lao hospitals. Funding The Wellcome Trust [Grant numbers 220211/Z/20/Z and 214207/Z/18/Z] and bioMérieux