A mean-field vaccination game scheme to analyze the effect of a single vaccination strategy on a two-strain epidemic spreading

2020 ◽  
Vol 2020 (3) ◽  
pp. 033501 ◽  
Author(s):  
Md Rajib Arefin ◽  
K M Ariful Kabir ◽  
Jun Tanimoto
Keyword(s):  
Mean Field ◽  
Vaccination Strategy ◽  
Epidemic Spreading ◽  
Single Vaccination ◽  
Game Scheme

scholarly journals A MEAN FIELD GAME ANALYSIS OF SIR DYNAMICS WITH VACCINATION

2020 ◽  
pp. 1-18
Author(s):  
Josu Doncel ◽  
Nicolas Gast ◽  
Bruno Gaujal
Keyword(s):  
Mean Field ◽  
Vaccination Strategy ◽  
Game Analysis ◽  
Total Cost ◽  
Mean Field Game ◽  
Vaccination Behavior ◽  
Switching Curve ◽  
The One ◽  
The Cost ◽  
Vaccination Period

We analyze a mean field game model of SIR dynamics (Susceptible, Infected, and Recovered) where players choose when to vaccinate. We show that this game admits a unique mean field equilibrium (MFE) that consists in vaccinating at a maximal rate until a given time and then not vaccinating. The vaccination strategy that minimizes the total cost has the same structure as the MFE. We prove that the vaccination period of the MFE is always smaller than the one minimizing the total cost. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized. Finally, we provide numerical experiments to study the convergence of the equilibrium when the system is composed by a finite number of agents ( $N$ ) to the MFE. These experiments show that the convergence rate of the cost is $1/N$ and the convergence of the switching curve is monotone.

scholarly journals Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0255438
Author(s):  
Vitor M. Marquioni ◽  
Marcus A. M. de Aguiar
Keyword(s):  
Population Genetics ◽  
Analytical Solution ◽  
Genetic Distance ◽  
Mean Field ◽  
Neutral Evolution ◽  
Genetic Evolution ◽  
Epidemic Spreading ◽  
Different Strains ◽  
Over Time ◽  
Good Agreement

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation that can be added directly to compartmental models such as SIR or SEIR to estimate the genetic evolution. We compare our results with the inferred genetic evolution of SARS-CoV-2 at the beginning of the epidemic in China and found good agreement with the analytical solution of our model. Finally, using genetic distance as a proxy for different strains, we use numerical simulations to show that the lower the connectivity between communities, e.g., cities, the higher the probability of reinfection.

EPIDEMIC SPREADING ON THREE-LAYER INTERDEPENDENT NETWORKS

2016 ◽  
Vol 24 (04) ◽  
pp. 469-494 ◽  
Author(s):  
LINGNA WANG ◽  
GUANGHU ZHU ◽  
HUIYAN KANG ◽  
XINCHU FU
Keyword(s):  
Infection Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mean Field ◽  
Network Size ◽  
Infection Rates ◽  
Epidemic Spreading ◽  
Interdependent Networks ◽  
Coupled Networks ◽  
The Basic Reproduction Number

Many epidemic diseases spread among three different populations with different contact patterns and infection rates. In response to such diseases, we propose two new types of three-layer interdependent networks — string-coupled networks and circular-coupled networks. We investigate an epidemic spreading on the two types of interdependent networks, propose two mathematical models through heterogeneous mean field approach and prove global stability of the disease-free and endemic equilibria. Through theoretical and numerical analysis, we find the following: the increase of each infection rate affects effectively only its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network for a fixed network size; but the change of the basic reproduction number (or the average infection densities) is almost the same on both string-coupled and circular-coupled networks with the increasing of certain infection rate.

scholarly journals IL-10 receptor blockade delivered simultaneous with BCG vaccination sustains long term protection against Mycobacterium tuberculosis infection in mice

2021 ◽  
Author(s):  
Varun Dwivedi ◽  
Shalini Gautam ◽  
Colwyn A. Headley ◽  
Tucker Piergallini ◽  
Jordi B Torrelles ◽  
...  
Keyword(s):  
Mycobacterium Tuberculosis ◽  
Vaccination Strategy ◽  
Interleukin 10 ◽  
Vaccine Strategy ◽  
Mycobacterium Tuberculosis Infection ◽  
Bcg Vaccination ◽  
Alternative Approach ◽  
Cytokine Levels ◽  
Single Vaccination

Mycobacterium bovis bacillus Calmette-Guérin (BCG) immunization still remains the best vaccination strategy available to control the development of active tuberculosis (TB). Protection afforded by BCG vaccination gradually wanes over time and while booster strategies have promise, they remain under development. An alternative approach is to improve BCG efficacy through host-directed therapy. Building upon prior knowledge that blockade of interleukin-10 receptor 1 (IL-10R1) during early Mycobacterium tuberculosis (M.tb) infection improves and extends control of M.tb infection in mice, we employed a combined anti-IL-10R1/BCG vaccine strategy. A subcutaneous, single vaccination of BCG/αIL10-R1 increased the numbers of CD4+ and CD8+ central memory T cells, and reduced TH1 and TH17 cytokine levels in the lung for up to 7 weeks post vaccination. Subsequent M.tb challenge in mice showed both an early (4 week) and sustained long-term (47 week) control of infection, which was associated with increased survival. In contrast, protection of BCG/saline vaccinated mice waned 8 weeks post M.tb infection. Our findings demonstrate that a single and simultaneous vaccination with BCG/αIL10-R1 sustains long-term protection, identifying a promising approach to enhance and extend the current BCG mediated protection against TB.

Research on SIQRS Spreading Dynamic Model with Feedback Mechanism on Scale-Free Networks

2014 ◽  
Vol 989-994 ◽  
pp. 4524-4527
Author(s):  
Tao Li ◽  
Yuan Mei Wang ◽  
You Ping Yang
Keyword(s):  
Dynamic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
The Relationship

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.

WEAK MEAN-FIELD APPROXIMATION FOR DISCRETE EPIDEMIC MODELS IN SCALE-FREE NETWORKS

2011 ◽  
Vol 19 (03) ◽  
pp. 403-416 ◽  
Author(s):  
QINGCHU WU ◽  
XINCHU FU
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Sis Epidemic Model ◽  
The Difference ◽  
Simple Difference ◽  
Previous Approximation

Epidemic dynamics in networks have attracted a great deal of attention from many fields. Based on the previous work, we propose a weak discrete mean-field approximation, and the difference with the previous approximation approach is that it can result in more simple difference equations. We mainly consider the minimal SIS epidemic model in complex networks, and make comparisons amongst two kinds of approximation formulations on the prediction of epidemic prevalence and find that they are effective to model epidemic spreading. Moreover, we investigate its application to the risk feedback case and simulations indicate its effectiveness.

Modelling immunization strategies with cytomegalovirus vaccine candidates

2011 ◽  
Vol 139 (12) ◽  
pp. 1818-1826 ◽  
Author(s):  
R. S. AZEVEDO ◽  
M. AMAKU
Keyword(s):  
Congenital Infection ◽  
Vaccination Strategy ◽  
Phase Ii Clinical Trials ◽  
Immunization Strategies ◽  
Current Vaccine ◽  
Single Vaccination ◽  
Mixing Patterns ◽  
Duration Of Protection ◽  
The Impact ◽  
Induced Immunity

SUMMARYIn order to analyse the impact of vaccination against cytomegalovirus (CMV) on congenital infection incidence using current vaccines tested in phase II clinical trials, we simulated different scenarios by mathematical modelling, departing from the current vaccine characteristics, varying age at vaccination, immunity waning, vaccine efficacy and mixing patterns. Our results indicated that the optimal age for a single vaccination interval is from 2 to 6 months if there is no immunity waning. Congenital infection may increase if vaccine-induced immunity wanes before 20 years. Congenital disease should increase further when the mixing pattern includes transmission among children with a short duration of protection vaccine. Thus, the best vaccination strategy is a combined schedule: before age 1 year plus a second dose at 10–11 years. For CMV vaccines with low efficacy, such as the current ones, universal vaccination against CMV should be considered for infants and teenagers.

The analysis of epidemic spreading on clique-overlapping growth network

2020 ◽  
Vol 34 (26) ◽  
pp. 2050235
Author(s):  
Zhenzhou Lin
Keyword(s):  
Theoretical Analysis ◽  
Mean Field Theory ◽  
Mean Field ◽  
Epidemic Outbreak ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Epidemic Dynamics ◽  
Immunization Strategies ◽  
The Mean ◽  
Real Complex

In this paper, we propose a new clique-overlapping growth network and study the epidemic spreading on it. We verify by simulation and theoretical analysis that the degree distribution follows a power-law form. Then, we have simulated the epidemic dynamics in this clique-overlapping growth network. Based on the mean-field theory, we have obtained the theoretical epidemic threshold. We find that the epidemic threshold is related to the evolution mechanism of the network model. The theoretical analysis is well consistent with the simulation results. The results in this model can help people understand the epidemic spreading of various processes, such as infectious diseases, computer viruses, gossips, and so on in real complex networks. Moreover, the appropriate immunization strategies can also be designed based on our results, to hold back the trend of epidemic outbreak.

Epidemic spreading of interacting diseases with activity of nodes reshapes the critical threshold

2017 ◽  
Vol 28 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Chongjun Fan ◽  
Yang Jin ◽  
Liang-An Huo ◽  
Chen Liu ◽  
Yunpeng Yang
Keyword(s):  
Temporal Evolution ◽  
Mean Field ◽  
Critical Threshold ◽  
Epidemic Spreading ◽  
Final Size ◽  
Node Activity ◽  
Transmission Rates ◽  
Field Approach ◽  
Spreading Dynamics ◽  
Theoretical Predictions

In this paper, based on susceptible–infected–susceptible (SIS) scheme, we introduce a framework that allows us to describe the spreading dynamics of two interacting diseases with active nodes. Different from previous studies, the two different diseases, propagating concurrently on the same population, can interact with each other by modifying their transmission rates. Meanwhile, according to certain probabilities, each node on the complex networks rotates between active state and inactive state. Based on heterogeneous mean-field approach, we analyze the epidemic thresholds of the two diseases and compute the temporal evolution characterizing the spreading dynamics. In addition, we validate these theoretical predictions by numerical simulations with phase diagrams. Results show that the secondary thresholds for the two opposite scenarios (mutual enhancement scenario and mutual impairment scenario) are different. We also find that the value of critical threshold and the final size of spreading dynamics are reduced as the node activity rate decreases.

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