A multi-group SEIRA model for the spread of COVID-19 among heterogeneous populations

The outbreak and propagation of COVID-19 have posed a considerable challenge to modern society. In particular, the different restrictive actions taken by governments to prevent the spread of the virus have changed the way humans interact and conceive interaction. Due to geographical, behavioral, or economic factors, different sub-groups among a population are more (or less) likely to interact, and thus to spread/acquire the virus. In this work, we present a general multi-group SEIRA model for representing the spread of COVID-19 among a heterogeneous population and test it in a numerical case of study. By highlighting its applicability and the ease with which its general formulation can be adapted to particular studies, we expect our model to lead us to a better understanding of the evolution of this pandemic and to better public-health policies to control it

Monte Carlo simulation of the transmission of measles: Beyond the mass action principle

We present a Monte Carlo simulation of the transmission of measles within a population sample during its growing and equilibrium states by introducing two different vaccination schedules of one and two doses. We study the effects of the contact rate per unit time $\xi$ as well as the initial conditions on the persistence of the disease. We found a weak effect of the initial conditions while the disease persists when $\xi$ lies in the range 1/L-10/L ($L$ being the latent period). Further comparison with existing data, prediction of future epidemics and other estimations of the vaccination efficiency are provided. Finally, we compare our approach to the models using the mass action principle in the first and another epidemic region and found the incidence independent of the number of susceptibles after the epidemic peak while it strongly fluctuates in its growing region. This method can be easily applied to other human, animals and vegetable diseases and includes more complicated parameters.Comment: 15 pages, 4 figures, 1 table, Submitted to Phys.Rev.

Saturation Effects and the Concurrency Hypothesis: Insights from an Analytic Model

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic populations with and without concurrency to allow for an investigation of its effects. Our models assume that partnerships change in time and individuals enter and leave the at-risk population. Infected individuals transmit at a constant per-partnership rate to their susceptible partners. In our idealized populations we find regions of parameter space where the existence of concurrent partnerships leads to substantially faster growth and higher equilibrium levels, but also regions in which the existence of concurrent partnerships has very little impact on the growth or the equilibrium. Additionally we find mixed regimes in which concurrency significantly increases the early growth, but has little effect on the ultimate equilibrium level. Guided by model predictions, we discuss general conditions under which concurrent relationships would be expected to have large or small effects in real-world settings. Our observation that the impact of concurrency saturates suggests that concurrency-reducing interventions may be most effective in populations with low to moderate concurrency

Modeling the Influence of Environment and Intervention on Cholera in Haiti

We propose a simple model with two infective classes in order to model the cholera epidemic in Haiti. We include the impact of environmental events (rainfall, temperature and tidal range) on the epidemic in the Artibonite and Ouest regions by introducing terms in the transmission rate that vary with environmental conditions. We fit the model on weekly data from the beginning of the epidemic until December 2013, including the vaccination programs that were recently undertaken in the Ouest and Artibonite regions. We then modified these projections excluding vaccination to assess the programs' effectiveness. Using real-time daily rainfall, we found lag times between precipitation events and new cases that range from 3.4 to 8.4 weeks in Artibonite and 5.1 to 7.4 in Ouest. In addition, it appears that, in the Ouest region, tidal influences play a significant role in the dynamics of the disease. Intervention efforts of all types have reduced case numbers in both regions; however, persistent outbreaks continue. In Ouest, where the population at risk seems particularly besieged and the overall population is larger, vaccination efforts seem to be taking hold more slowly than in Artibonite, where a smaller core population was vaccinated. The models including the vaccination programs predicted that a year and six months later, the mean number of cases in Artibonite would be reduced by about two thousand cases, and in Ouest by twenty four hundred cases below that predicted by the models without vaccination. We also found that vaccination is best when done in the early spring, and as early as possible in the epidemic. Comparing vaccination between the first spring and the second, there is a drop of about 40% in the case reduction due to the vaccine and about 10% per year after that

SimInf: An R package for Data-driven Stochastic Disease Spread Simulations

We present the R package SimInf which provides an efficient and very flexible framework to conduct data-driven epidemiological modeling in realistic large scale disease spread simulations. The framework integrates infection dynamics in subpopulations as continuous-time Markov chains using the Gillespie stochastic simulation algorithm and incorporates available data such as births, deaths and movements as scheduled events at predefined time-points. Using C code for the numerical solvers and OpenMP to divide work over multiple processors ensures high performance when simulating a sample outcome. One of our design goal was to make SimInf extendable and enable usage of the numerical solvers from other R extension packages in order to facilitate complex epidemiological research. In this paper, we provide a technical description of the framework and demonstrate its use on some basic examples. We also discuss how to specify and extend the framework with user-defined models.Comment: The manual has been updated to the latest version of SimInf (v6.0.0). 41 pages, 16 figure

Global stability for epidemic model with constant latency and infectious periods.

In recent years many delay epidemiological models have been proposed to study at which stage of the epidemics the delays can destabilize the disease free equilibrium, or the endemic equilibrium, giving rise to stability switches. One of these models is the SEIR model with constant latency time and infectious periods [2], for which the authors have proved that the two delays are harmless in inducing stability switches. However, it is left open the problem of the global asymptotic stability of the endemic equilibrium whenever it exists. Even the Lyapunov functions approach, recently proposed by Huang and Takeuchi to study many delay epidemiological models, fails to work on this model. In this paper, an age-infection model is presented for the delay SEIR epidemic model, such that the properties of global asymptotic stability of the equilibria of the age-infection model imply the same properties for the original delay-differential epidemic model. By introducing suitable Lyapunov functions to study the global stability of the disease free equilibrium (when $\mathcal{R}_0\leq 1$) and of the endemic equilibria (whenever $\mathcal{R}_0>1$) of the age-infection model, we can infer the corresponding global properties for the equilibria of the delay SEIR model in [2], thus proving that the endemic equilibrium in [2] is globally asymptotically stable whenever it exists. &nbsp Furthermore, we also present a review of the SIR, SEIR epidemic models, with and without delays, appeared in literature, that can be seen as particular cases of the approach presented in the paper

Stability analysis of drinking epidemic models and investigation of optimal treatment strategy

In this research we investigate a class of drinking epidemic models, namely the SPARS type models. The basic reproduction number is derived, and the system dynamical behaviours are investigated for both drinking free equilibrium and drinking persistent equilibrium. The purpose is to determine the long term optimal treatment method and the optimal short period vaccination strategy for controlling the population of the periodic drinkers and alcoholics

Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay

This paper aims to discuss the delay epidemic model with vertical transmission, constant input, and nonlinear incidence. Some sufficient conditions are given to guarantee the existence and global attractiveness of the infection-free periodic solution and the uniform persistence of the addressed model with time delay. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results