A stochastic SIR network epidemic model with preventive dropping of edges

Abstract

A Markovian Susceptible Infectious Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size , assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy–Reed (in which the degrees of individuals are deterministic) and Newman–Strogatz–Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman–Strogatz–Watts version. The basic reproduction number and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when , the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N .

The prevalence of pregnancy among adolescent girls and young women across the Southern African development community economic hub: A systematic review and meta-analysis

“…We calculated prevalence for each included study by dividing the number of AGYW ever pregnant (n) by the total number of AGYW in the study sample and expressed it as percent. 63,78 The sampling distribution for the prevalence statistic was assumed to have a normal distribution since the sample sizes were large enough to assume Central Limit Theorem. 63,78 Using STATA 13.1 (StataCorp, Texas, USA), the prevalence of pregnancy from the different studies were pooled in a random effects meta-analysis since we anticipated heterogeneity owing to the studies in different countries and settings.…”

“…63,78 The sampling distribution for the prevalence statistic was assumed to have a normal distribution since the sample sizes were large enough to assume Central Limit Theorem. 63,78 Using STATA 13.1 (StataCorp, Texas, USA), the prevalence of pregnancy from the different studies were pooled in a random effects meta-analysis since we anticipated heterogeneity owing to the studies in different countries and settings. We applied the I 2 test statistic which estimates the percentage of variation that is due to heterogeneity rather than the chance occurrences, where values exceeding 50% indicate significant heterogeneity.…”

“…We calculated prevalence for each included study by dividing the number of AGYW ever pregnant (n) by the total number of AGYW in the study sample and expressed it as percent. 63 , 78 …”

COVID-19 Spread in Saudi Arabia: Modeling, Simulation and Analysis

“…Read and Keeling [ 37 ] investigated how local or global transmission routes in a contact network may affect the evolutionary selection of the transmission rate and infectious period, which determines the transmission dynamics of infectious diseases. Ball et al [ 38 ] proposed a stochastic SIR network epidemic model with preventive dropping, where a susceptible individual can practice social distancing by removing its edge to an infectious individual. Due to the importance of social mixing patterns on modeling epidemic dynamics and evaluating the employed control measures, many research efforts have been made to estimate the patterns in different countries [ 39 , 40 , 41 , 42 ].…”

Balancing quarantine and self-distancing measures in adaptive epidemic networks

“…Of course, many generalizations of the presented model are possible. For example, one could try to use slightly different rules for the link dynamics allowing for link deletion [BBLS19, TW13]. Yet, we conjecture that the same analysis principles we have developed here still apply.…”