scholarly journals Number of infections suffered by a focal individual in a two‐strain SIS model with partial cross‐immunity

2019 ◽  
Vol 42 (12) ◽  
pp. 4318-4330 ◽  
Author(s):  
Elena Almaraz ◽  
Antonio Gómez‐Corral
Keyword(s):  
Sis Model ◽  
Focal Individual ◽  
Cross Immunity

SIS model

2018 ◽  
Keyword(s):  
Sis Model

Optimal Cybersecurity Investments for SIS Model

2020 ◽  
Author(s):  
Van Sy Mai ◽  
Richard J. La ◽  
Abdella Battou
Keyword(s):  
Sis Model

scholarly journals A Stochastic Kinetic Type Reactions Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1221
Author(s):  
Giorgio Sonnino ◽  
Fernando Mora ◽  
Pasquale Nardone
Keyword(s):  
Real Data ◽  
Stochastic Noise ◽  
Mathematical Basis ◽  
Sis Model ◽  
Theoretical Predictions ◽  
Coronavirus Infection ◽  
Massive Distribution ◽  
Second Wave ◽  
Stochastic Sis Model

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) and the stochastic SIS-model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

scholarly journals Secure the IoT Networks as Epidemic Containment Game

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 156
Author(s):  
Juntao Zhu ◽  
Hong Ding ◽  
Yuchen Tao ◽  
Zhen Wang ◽  
Lanping Yu
Keyword(s):  
Heuristic Algorithms ◽  
Heuristic Method ◽  
Exact Algorithms ◽  
Epidemic Threshold ◽  
Solution Quality ◽  
Sis Model ◽  
Linear Programming Formulation ◽  
Iot Devices ◽  
General Graphs ◽  
The Internet Of Things

The spread of a computer virus among the Internet of Things (IoT) devices can be modeled as an Epidemic Containment (EC) game, where each owner decides the strategy, e.g., installing anti-virus software, to maximize his utility against the susceptible-infected-susceptible (SIS) model of the epidemics on graphs. The EC game’s canonical solution concepts are the Minimum/Maximum Nash Equilibria (MinNE/MaxNE). However, computing the exact MinNE/MaxNE is NP-hard, and only several heuristic algorithms are proposed to approximate the MinNE/MaxNE. To calculate the exact MinNE/MaxNE, we provide a thorough analysis of some special graphs and propose scalable and exact algorithms for general graphs. Especially, our contributions are four-fold. First, we analytically give the MinNE/MaxNE for EC on special graphs based on spectral radius. Second, we provide an integer linear programming formulation (ILP) to determine MinNE/MaxNE for the general graphs with the small epidemic threshold. Third, we propose a branch-and-bound (BnB) framework to compute the exact MinNE/MaxNE in the general graphs with several heuristic methods to branch the variables. Fourth, we adopt NetShiled (NetS) method to approximate the MinNE to improve the scalability. Extensive experiments demonstrate that our BnB algorithm can outperform the naive enumeration method in scalability, and the NetS can improve the scalability significantly and outperform the previous heuristic method in solution quality.

scholarly journals COLORADO TICK FEVER AND DENGUE

1946 ◽  
Vol 83 (4) ◽  
pp. 295-301 ◽  
Author(s):  
Lloyd Florio ◽  
William McD. Hammon ◽  
Angela Laurent ◽  
Mabel O. Stewart
Keyword(s):  
Endemic Area ◽  
Human Beings ◽  
Distinct Disease ◽  
Disease Entities ◽  
Cross Immunity

Six human beings were inoculated with dengue and developed typical disease. Two of these were reinoculated and proved immune. The remaining four were later inoculated with Colorado tick fever. Three developed typical disease. The fourth, who remained well, has previously lived in an endemic area (Colorado). One patient was inoculated with Colorado tick fever first and later with dengue. He developed both diseases. Colorado tick fever and dengue do not give a cross-immunity. Hamsters can be infected with Colorado tick fever but not with dengue. Colorado tick fever and dengue appear to be distinct disease entities.

scholarly journals Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 888
Author(s):  
Jumpei Inoue ◽  
Kousuke Kuto
Keyword(s):  
Recovery Rate ◽  
Regional Difference ◽  
Total Population ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Logistic Equation ◽  
Sis Model ◽  
Reaction Diffusion Model ◽  
Diffusive Logistic Equation ◽  
Sis Epidemic

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

scholarly journals Prevalence and Cross-Immunity of Eimeria Species on Korean Chicken Farms

2010 ◽  
Vol 72 (8) ◽  
pp. 985-989 ◽  
Author(s):  
Byung H. LEE ◽  
Woo H. KIM ◽  
Jipseol JEONG ◽  
Jeongmi YOO ◽  
Yong-Kuk KWON ◽  
...  
Keyword(s):  
Eimeria Species ◽  
Cross Immunity

scholarly journals Who directs group movement? Leader effort versus follower preference in stickleback fish of different personality

2016 ◽  
Vol 12 (5) ◽  
pp. 20160207 ◽  
Author(s):  
Shinnosuke Nakayama ◽  
Jennifer L. Harcourt ◽  
Rufus A. Johnstone ◽  
Andrea Manica
Keyword(s):  
Collective Movement ◽  
Group Movement ◽  
Focal Individual ◽  
Focal Fish ◽  
Set Up

During collective movement, bolder individuals often emerge as leaders. Here, we investigate whether this reflects a greater propensity of bold individuals to initiate movement, or a preference for shy individuals to follow a bolder leader. We set up trios of stickleback fish comprising a focal individual who was either bold or shy, and one other individual of each personality. We then recorded the movements of all individuals in and out of cover in a foraging context to determine how assiduously the focal fish followed the movements of each other partner. We found that a shy focal fish preferred to follow a leader whose personality matched its own, but we did not detect such a difference in bold fish. Despite this preference, however, the greater propensity of bold individuals to initiate movements out of cover meant that they successfully led more joint trips. Thus, when offered a choice of leaders, sticklebacks prefer to follow individuals whose personality matches their own, but bolder individuals may, nevertheless, be able to impose their leadership, even among shy followers, simply through greater effort.

scholarly journals Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Yanju Xiao ◽  
Weipeng Zhang ◽  
Guifeng Deng ◽  
Zhehua Liu
Keyword(s):  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sis Model ◽  
Delayed Treatment ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Lyapunov Coefficient ◽  
Saturated Treatment ◽  
Theoretical Results ◽  
Disease Free

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

scholarly journals A COMPARATIVE STUDY OF RECENTLY ISOLATED HUMAN STRAINS AND A PASSAGE STRAIN OF POLIOMYELITIS VIRUS

1933 ◽  
Vol 58 (5) ◽  
pp. 513-529 ◽  
Author(s):  
John R. Paul ◽  
James D. Trask
Keyword(s):  
Comparative Study ◽  
Human Strain ◽  
Time Interval ◽  
Subsequent Infection ◽  
Poliomyelitis Virus ◽  
Intracerebral Inoculation ◽  
Human Sera ◽  
Cross Immunity ◽  
Experimental Disease

1. Confirmation of the qualitative differences which exist between so called human and passage strains of poliomyelitis virus has been established by the following observations. (a) The experimental disease induced by two human strains usually failed to protect monkeys against a subsequent infection by a passage strain, and in the few instances in which the reverse experiment could be tried a similar lack of protection was observed. (b) In some human sera the neutralizing power for a human strain differed qualitatively from the neutralizing power for a passage strain. 2. The time interval between the intracerebral inoculation of heterologous strains has been found to be an important factor bearing upon the results of the reinoculation experiments reported. Within the intervals used, the greater the period between the original infection and the reinoculation with a heterologous strain, the less was the degree of cross-immunity observed.

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