TIME-VARYING EPIDEMIC TRANSMISSION IN HETEROGENEOUS NETWORKS AND APPLICATIONS TO MEASLES

2020 ◽  
Vol 28 (04) ◽  
pp. 901-926
Author(s):  
SARA SOTTILE ◽  
XINZHI LIU

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the behavior of the time-weighted average Basic Reproduction Number (BRN). Later, a Susceptible–Exposed–Infectious–Recovered (SEIR) model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we can find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behavior of the switching rule, we compare the results with the BRN of the model. Some simulations are given, using a scale-free network, to illustrate the threshold conditions found.

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Chao Zuo ◽  
Anjing Wang ◽  
Fenping Zhu ◽  
Zeyang Meng ◽  
Xueke Zhao

In this paper, we propose a nonlinear coupled model to study the two interacting processes of awareness diffusion and epidemic spreading on the same individual who is affected by different neighbor behavior status on multiplex networks. We achieve this topology scenario by two kinds of factors, one is the perception factor that can change interplay between different layers of networks and the other is the neighbors’ behavior status that can change the infection rate in each layer. According to the microscopic Markov chain approach (MMCA), we analyze the dynamical evolution of the system and derive the theoretical epidemic threshold on uncorrelated heterogeneous networks, and then, we validate the analysis by numerical simulation and discuss the final size of awareness diffusion and epidemic spreading on a scale-free network. With the outbreak of COVID-19, the spread of epidemic in China prompted drastic measures for transmission containment. We examine the effects of these interventions based on modeling of the awareness-epidemic and the COVID-19 epidemic case. The results further demonstrate that the epidemic spreading can be affected by the effective transmission rate of the awareness and neighbors’ behavior status.


2015 ◽  
Vol 29 (08) ◽  
pp. 1550023 ◽  
Author(s):  
Fuzhong Nian ◽  
Ke Wang

In this paper, a new immunization strategy was established to prevent the epidemic spreading based on the principle of "Multi-granularity" and "Pre-warning Mechanism", which send different pre-warning signal with the risk rank of the susceptible node to be infected. The pre-warning means there is a higher risk that the susceptible node is more likely to be infected. The multi-granularity means the susceptible node is linked with multi-infected nodes. In our model, the effect of the different situation of the multi-granularity immunizations is compared and different spreading rates are adopted to describe the epidemic behavior of nodes. In addition the threshold value of epidemic outbreak is investigated, which makes the result more convincing. The theoretical analysis and the simulations indicate that the proposed immunization strategy is effective and it is also economic and feasible.


2009 ◽  
Vol 29 (5) ◽  
pp. 1230-1232
Author(s):  
Hao RAO ◽  
Chun YANG ◽  
Shao-hua TAO

2017 ◽  
Vol 27 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Jennifer C. Urquhart ◽  
Osama A. Alrehaili ◽  
Charles G. Fisher ◽  
Alyssa Fleming ◽  
Parham Rasoulinejad ◽  
...  

OBJECTIVEA multicenter, prospective, randomized equivalence trial comparing a thoracolumbosacral orthosis (TLSO) to no orthosis (NO) in the treatment of acute AO Type A3 thoracolumbar burst fractures was recently conducted and demonstrated that the two treatments following an otherwise similar management protocol are equivalent at 3 months postinjury. The purpose of the present study was to determine whether there was a difference in long-term clinical and radiographic outcomes between the patients treated with and those treated without a TLSO. Here, the authors present the 5- to 10-year outcomes (mean follow-up 7.9 ± 1.1 years) of the patients at a single site from the original multicenter trial.METHODSBetween July 2002 and January 2009, a total of 96 subjects were enrolled in the primary trial and randomized to two groups: TLSO or NO. Subjects were enrolled if they had an AO Type A3 burst fracture between T-10 and L-3 within the previous 72 hours, kyphotic deformity < 35°, no neurological deficit, and an age of 16–60 years old. The present study represents a subset of those patients: 16 in the TLSO group and 20 in the NO group. The primary outcome measure was the Roland Morris Disability Questionnaire (RMDQ) score at the last 5- to 10-year follow-up. Secondary outcome measures included kyphosis, satisfaction, the Numeric Rating Scale for back pain, and the 12-Item Short-Form Health Survey (SF-12) Mental and Physical Component Summary (MCS and PCS) scores. In the original study, outcome measures were administered at admission and 2 and 6 weeks, 3 and 6 months, and 1 and 2 years after injury; in the present extended follow-up study, the outcome measures were administered 5–10 years postinjury. Treatment comparison between patients in the TLSO group and those in the NO group was performed at the latest available follow-up, and the time-weighted average treatment effect was determined using a mixed-effects model of longitudinal regression for repeated measures averaged over all time periods. Missing data were assumed to be missing at random and were replaced with a set of plausible values derived using a multiple imputation procedure.RESULTSThe RMDQ score at 5–10 years postinjury was 3.6 ± 0.9 (mean ± SE) for the TLSO group and 4.8 ± 1.5 for the NO group (p = 0.486, 95% CI −2.3 to 4.8). Average kyphosis was 18.3° ± 2.2° for the TLSO group and 18.6° ± 3.8° for the NO group (p = 0.934, 95% CI −7.8 to 8.5). No differences were found between the NO and TLSO groups with time-weighted average treatment effects for RMDQ 1.9 (95% CI −1.5 to 5.2), for PCS −2.5 (95% CI −7.9 to 3.0), for MCS −1.2 (95% CI −6.7 to 4.2) and for average pain 0.9 (95% CI −0.5 to 2.2).CONCLUSIONSCompared with patients treated with a TLSO, patients treated using early mobilization without orthosis maintain similar pain relief and improvement in function for 5–10 years.


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