A Simple Model of Epidemics with Pathogen Mutation

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals, (2) endemic infection (3) periodic epidemic outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.Comment: 9 pages, 11 figure

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Achieving coordinated national immunity and cholera elimination in Haiti through vaccination: a modelling study

Background: Cholera was introduced into Haiti in 2010. Since then, more than 820 000 cases and nearly 10 000 deaths have been reported. Oral cholera vaccine (OCV) is safe and effective, but has not been seen as a primary tool for cholera elimination due to a limited period of protection and constrained supplies. Regionally, epidemic cholera is contained to the island of Hispaniola, and the lowest numbers of cases since the epidemic began were reported in 2019. Hence, Haiti may represent a unique opportunity to eliminate cholera with OCV. Methods: In this modelling study, we assessed the probability of elimination, time to elimination, and percentage of cases averted with OCV campaign scenarios in Haiti through simulations from four modelling teams. For a 10-year period from January 19, 2019, to Jan 13, 2029, we compared a no vaccination scenario with five OCV campaign scenarios that differed in geographical scope, coverage, and rollout duration. Teams used weekly department-level reports of suspected cholera cases from the Haiti Ministry of Public Health and Population to calibrate the models and used common vaccine-related assumptions, but other model features were determined independently. Findings: Among campaigns with the same vaccination coverage (70% fully vaccinated), the median probability of elimination after 5 years was 0–18% for no vaccination, 0–33% for 2-year campaigns focused in the two departments with the highest historical incidence, 0–72% for three-department campaigns, and 35–100% for nationwide campaigns. Two-department campaigns averted a median of 12–58% of infections, three-department campaigns averted 29–80% of infections, and national campaigns averted 58–95% of infections. Extending the national campaign to a 5-year rollout (compared to a 2-year rollout), reduced the probability of elimination to 0–95% and the proportion of cases averted to 37–86%. Interpretation: Models suggest that the probability of achieving zero transmission of Vibrio cholerae in Haiti with current methods of control is low, and that bolder action is needed to promote elimination of cholera from the region. Large-scale cholera vaccination campaigns in Haiti would offer the opportunity to synchronise nationwide immunity, providing near-term population protection while improvements to water and sanitation promote long-term cholera elimination. Funding: Bill & Melinda Gates Foundation, Global Good Fund, Institute for Disease Modeling, Swiss National Science Foundation, and US National Institutes of Health

Use of immunological markers and continuous-time Markov models to estimate progression of HIV infection in homosexual men

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A Delay Differential Model for Pandemic Influenza with Antiviral Treatment

The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the density of infected individuals in terms of the time elapsed since the onset of symptoms. We show that such a model can be expressed by a system of delay differential equations with both discrete and distributed delays. The model is analyzed to derive the criterion for disease control based on two critical factors: (i) the profile of treatment rate; and (ii) the level of treatment as a function of time lag in commencing therapy. Numerical results are also obtained to illustrate the feasible region of disease control. Our findings show that due to uncertainty in the attack rate of a pandemic strain, initiating therapy immediately upon diagnosis can significantly increase the likelihood of disease control and substantially reduce the required community-level of treatment. This suggests that reliable diagnostic methods for influenza cases should be rapidly implemented within an antiviral treatment strategy

Large Sample Randomization Inference of Causal Effects in the Presence of Interference

Recently, increasing attention has focused on making causal inference when interference is possible. In the presence of interference, treatment may have several types of effects. In this paper, we consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups. A two stage randomization design is assumed where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage. For this design, the asymptotic distributions of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large. Under certain homogeneity assumptions, the asymptotic distributions provide justification for Wald-type confidence intervals (CIs) and tests. Empirical results demonstrate the Wald CIs have good coverage in finite samples and are narrower than CIs based on either the Chebyshev or Hoeffding inequalities provided the number of groups is not too small. The methods are illustrated by two examples which consider the effects of cholera vaccination and an intervention to encourage voting

Creating a framework for conducting randomized clinical trials during disease outbreaks

As in the ongoing Covid-19 pandemic, global outbreaks of infectious illnesses often develop quickly and resolve in unpredictable ways. In this report, strategies to develop high-quality evidence to guide the development of new therapies are proposed