scholarly journals The stationary distribution and stochastic persistence for a class of disease models: Case study of malaria

2020 ◽  
Vol 13 (04) ◽  
pp. 2050024
Author(s):  
Divine Wanduku
Keyword(s):  
Stationary Distribution ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Statistical Characteristics ◽  
Local Martingale ◽  
Natural Death ◽  
Death Rates ◽  
Plasmodium Vivax Malaria ◽  
Over Time

This paper presents a nonlinear family of stochastic SEIRS models for diseases such as malaria in a highly random environment with noises from the disease transmission and natural death rates, and also from the random delays of the incubation and immunity periods. Improved analytical methods and local martingale characterizations are applied to find conditions for the disease to persist near an endemic steady state, and also for the disease to remain permanently in the system over time. Moreover, the ergodic stationary distribution for the stochastic process describing the disease dynamics is defined, and the statistical characteristics of the distribution are given numerically. The results of this study show that the disease will persist and become permanent in the system, regardless of (1) whether the noises are from the disease transmission rate and/or from the natural death rates or (2) whether the delays in the system are constant or random for individuals in the system. Furthermore, it is shown that “weak” noise is associated with the existence of an endemic stationary distribution for the disease, while “strong” noise is associated with extinction of the population over time. Numerical simulation examples for Plasmodium vivax malaria are given.

scholarly journals Transmission frequency of covid-19 through pre-symptomatic and asymptomatic patients in AJK: A report of 201 cases

2021 ◽  
Author(s):  
Majid Mahmood ◽  
Noor-ul-ain Ilyas ◽  
Muhammad Khan ◽  
Muhammad Hasrat
Keyword(s):  
Disease Transmission ◽  
Human Population ◽  
Virus Disease ◽  
Transmission Rate ◽  
Retrospective Case ◽  
Transmission Frequency ◽  
Infection Transmission ◽  
Asymptomatic Patients ◽  
History Of

Abstract Background: Corona virus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2, declared as “once-in-a-century” pandemic, has affected about entire human population. Till now, the most promising control strategy is to block the transmission which will never be effective without completely knowing the transmission patterns.Methods: This was a retrospective case to case study aiming to estimate and calculate the transmission rate of COVID-19 through pre-symptomatic and asymptomatic patients. Contact history of included positive cases during the period of 24 hours before appearance of symptoms and infection confirmation for symptomatic and asymptomatic cases respectively was traced for disease transmission. Results: Overall, a total of 201 cases had contacted with 7168 people in last 24 hours with an average of 35.66 contacts per patient ranging from a minimum of 4 to maximum of 87 contacts (Meetings). Out of 7168 meeting persons, the infection was traced in 64 (0.89%) persons. For 155 symptomatic patients, a total of 5611 contacting persons were traced before appearance of symptoms (pre-symptomatic) in last 24 hours with an average of 36.20 meetings per patient. The infection was transmitted in 63 (1.12%) people and remaining 5548 (98.88%) were remained uninfected. Out of the 63 transmissions, 62 (98.4%) were traced within last 6 hours before the onset of symptoms while only 1 was traced from 6-12 hours before symptoms. A total of 1557 persons were traced having meeting/contacts with asymptomatic cases in last 24 hours before their infection confirmation. Out of these 1557 persons, only 1 was found to be infected and the infection rate was calculated to be 0.06%. Conclusion: The study concludes that the risk of pre-symptomatic transmission of infection is low (1.12%) and it becomes very rare in contacts made longer than 6 hours before onset of symptoms. The infection transmission is traced as long as about 9 hours before the appearance of clear symptoms in the patients but the incidence was as low as about 0.02% of the total contacts in that period. Transmission frequency by asymptomatic patients is also rare (0.06%) in the studied population.

scholarly journals Transmission frequency of COVID-19 through pre-symptomatic and asymptomatic patients in AJK: A report of 201 cases

2021 ◽  
Author(s):  
Majid Mahmood ◽  
Noor-ul-ain Ilyas ◽  
Muhammad Faraz Khan ◽  
Muhammad Naseem Hasrat
Keyword(s):  
Disease Transmission ◽  
Human Population ◽  
Virus Disease ◽  
Transmission Rate ◽  
Retrospective Case ◽  
Transmission Frequency ◽  
Infection Transmission ◽  
Asymptomatic Patients ◽  
History Of

Abstract Background: Corona virus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2, declared as “once-in-a-century” pandemic, has affected about entire human population. Till now, the most promising control strategy is to block the transmission which will never be effective without completely knowing the transmission patterns.Methods: This was a retrospective case to case study aiming to estimate and calculate the transmission rate of COVID-19 through pre-symptomatic and asymptomatic patients. Contact history of included positive cases during the period of 24 hours before appearance of symptoms and infection confirmation for symptomatic and asymptomatic cases respectively was traced for disease transmission. Results: Overall, a total of 201 cases had contacted with 7168 people in last 24 hours with an average of 35.66 contacts per patient ranging from a minimum of 4 to maximum of 87 contacts (Meetings). Out of 7168 meeting persons, the infection was traced in 64 (0.89%) persons. For 155 symptomatic patients, a total of 5611 contacting persons were traced before appearance of symptoms (pre-symptomatic) in last 24 hours with an average of 36.20 meetings per patient. The infection was transmitted in 63 (1.12%) people and remaining 5548 (98.88%) were remained uninfected. Out of the 63 transmissions, 62 (98.4%) were traced within last 6 hours before the onset of symptoms while only 1 was traced from 6-12 hours before symptoms. A total of 1557 persons were traced having meeting/contacts with asymptomatic cases in last 24 hours before their infection confirmation. Out of these 1557 persons, only 1 was found to be infected and the infection rate was calculated to be 0.06%. Conclusion: The study concludes that the risk of pre-symptomatic transmission of infection is low (1.12%) and it becomes very rare in contacts made longer than 6 hours before onset of symptoms. The infection transmission is traced as long as about 9 hours before the appearance of clear symptoms in the patients but the incidence was as low as about 0.02% of the total contacts in that period. Transmission frequency by asymptomatic patients is also rare (0.06%) in the studied population.

scholarly journals Transmission frequency of covid-19 through pre-symptomatic and asymptomatic patients in AJK: A report of 201 cases

2021 ◽  
Author(s):  
Majid Mahmood ◽  
Noor-ul-ain Ilyas ◽  
Muhammad Faraz Khan ◽  
Muhammad Naseem Hasrat
Keyword(s):  
Disease Transmission ◽  
Human Population ◽  
Virus Disease ◽  
Transmission Rate ◽  
Retrospective Case ◽  
Transmission Frequency ◽  
Infection Transmission ◽  
Asymptomatic Patients ◽  
History Of

Abstract Background: Corona virus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2, declared as “once-in-a-century” pandemic, has affected about entire human population. Till now, the most promising control strategy is to block the transmission which will never be effective without completely knowing the transmission patterns.Methods: This was a retrospective case to case study aiming to estimate and calculate the transmission rate of COVID-19 through pre-symptomatic and asymptomatic patients. Contact history of included positive cases during the period of 24 hours before appearance of symptoms and infection confirmation for symptomatic and asymptomatic cases respectively was traced for disease transmission. Results: Overall, a total of 201 cases had contacted with 7168 people in last 24 hours with an average of 35.66 contacts per patient ranging from a minimum of 4 to maximum of 87 contacts (Meetings). Out of 7168 meeting persons, the infection was traced in 64 (0.89%) persons. For 155 symptomatic patients, a total of 5611 contacting persons were traced before appearance of symptoms (pre-symptomatic) in last 24 hours with an average of 36.20 meetings per patient. The infection was transmitted in 63 (1.12%) people and remaining 5548 (98.88%) were remained uninfected. Out of the 63 transmissions, 62 (98.4%) were traced within last 6 hours before the onset of symptoms while only 1 was traced from 6-12 hours before symptoms. A total of 1557 persons were traced having meeting/contacts with asymptomatic cases in last 24 hours before their infection confirmation. Out of these 1557 persons, only 1 was found to be infected and the infection rate was calculated to be 0.06%. Conclusion: The study concludes that the risk of pre-symptomatic transmission of infection is low (1.12%) and it becomes very rare in contacts made longer than 6 hours before onset of symptoms. The infection transmission is traced as long as about 9 hours before the appearance of clear symptoms in the patients but the incidence was as low as about 0.02% of the total contacts in that period. Transmission frequency by asymptomatic patients is also rare (0.06%) in the studied population.

scholarly journals Estimating Time-Dependent Disease Transmission Intensity using Reported Data: An Application to Ebola and Selected Public Health Problems

2021 ◽  
Author(s):  
Aditi Ghosh ◽  
Anuj Mubayi ◽  
Abhishek Pandey ◽  
Christine Brasic ◽  
Anamika Mubayi ◽  
...  
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Disease Transmission ◽  
Social Issues ◽  
Transmission Rate ◽  
Health Problems ◽  
Time Dependent ◽  
Transmission Rates ◽  
Reported Data ◽  
Over Time

Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of infectious diseases, like Ebola. Most models assume the transmission rate of a contagion does not vary over time. However, these rates do vary during an epidemic due to environmental conditions, social behaviors, and public-health interventions deployed to control the disease. Therefore, obtaining time-dependent rates can aid in understanding the progression of disease through a population. We derive an analytical expression using a standard SIR-type mathematical model to compute time-dependent transmission rate estimates for an epidemic in terms of either incidence or prevalence type available data. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that transmission rate estimates can have a large variation over time, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem and can be utilized to understand disease progression through population accurately. Alternatively, constant estimations may provide unacceptable results that could have major public health consequences.

scholarly journals Transmission frequency of covid-19 through pre-symptomatic and asymptomatic patients in AJK: A report of 201 cases

2021 ◽  
Author(s):  
Majid Mahmood ◽  
Noor-ul-ain Ilyas ◽  
Muhammad Faraz Khan ◽  
Muhammad Naseem Hasrat
Keyword(s):  
Disease Transmission ◽  
Human Population ◽  
Virus Disease ◽  
Transmission Rate ◽  
Retrospective Case ◽  
Transmission Frequency ◽  
Infection Transmission ◽  
Asymptomatic Patients ◽  
History Of

Abstract Background: Corona virus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2, declared as “once-in-a-century” pandemic, has affected about entire human population. Till now, the most promising control strategy is to block the transmission which will never be effective without completely knowing the transmission patterns.Methods: This was a retrospective case to case study aiming to estimate and calculate the transmission rate of COVID-19 through pre-symptomatic and asymptomatic patients. Contact history of included positive cases during the period of 24 hours before appearance of symptoms and infection confirmation for symptomatic and asymptomatic cases respectively was traced for disease transmission. Results: Overall, a total of 201 cases had contacted with 7168 people in last 24 hours with an average of 35.66 contacts per patient ranging from a minimum of 4 to maximum of 87 contacts (Meetings). Out of 7168 meeting persons, the infection was traced in 64 (0.89%) persons. For 155 symptomatic patients, a total of 5611 contacting persons were traced before appearance of symptoms (pre-symptomatic) in last 24 hours with an average of 36.20 meetings per patient. The infection was transmitted in 63 (1.12%) people and remaining 5548 (98.88%) were remained uninfected. Out of the 63 transmissions, 62 (98.4%) were traced within last 6 hours before the onset of symptoms while only 1 was traced from 6-12 hours before symptoms. A total of 1557 persons were traced having meeting/contacts with asymptomatic cases in last 24 hours before their infection confirmation. Out of these 1557 persons, only 1 was found to be infected and the infection rate was calculated to be 0.06%. Conclusion: The study concludes that the risk of pre-symptomatic transmission of infection is low (1.12%) and it becomes very rare in contacts made longer than 6 hours before onset of symptoms. The infection transmission is traced as long as about 9 hours before the appearance of clear symptoms in the patients but the incidence was as low as about 0.02% of the total contacts in that period. Transmission frequency by asymptomatic patients is also rare (0.06%) in the studied population.

scholarly journals Analytical Estimation of Data-Motivated Time-Dependent Disease Transmission Rate: An Application to Ebola and Selected Public Health Problems

2021 ◽  
Vol 6 (3) ◽  
pp. 141
Author(s):  
Anuj Mubayi ◽  
Abhishek Pandey ◽  
Christine Brasic ◽  
Anamika Mubayi ◽  
Parijat Ghosh ◽  
...  
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Disease Transmission ◽  
Social Issues ◽  
Transmission Rate ◽  
Health Problems ◽  
Time Dependent ◽  
Transmission Rates ◽  
Analytical Estimation ◽  
Over Time

Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of ?infectious? diseases, like Ebola. Most models assume the transmission rate of a contagion either does not vary over time or change in a fixed pre-determined adhoc ways. However, these rates do vary during an outbreak due to multitude of factors such as environmental conditions, social behaviors, and public-health interventions deployed to control the disease, which are in-part guided by changing size of an outbreak. We derive analytical estimates of time-dependent transmission rate for an epidemic in terms of either incidence or prevalence using a standard mathematical SIR-type epidemic model. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that time-dependent transmission rate estimates can have a large variation, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem better and can be utilized to understand disease progression more accurately.

When Culturally Significant Songs are Decontextualised: The Initiation Song Somagwaza, A Case Study

2018 ◽  
Vol 28 (2) ◽  
Author(s):  
T Dowling ◽  
Somikazi Deyi ◽  
Anele Gobodwana
Keyword(s):  
Qualitative Research ◽  
Comparative Method ◽  
Popular Song ◽  
Focus Group Discussions ◽  
Group Discussions ◽  
Ritual Music ◽  
Constant Comparative Method ◽  
Small Focus ◽  
Over Time

While there have been a number of studies on the decontextualisation and secularisation of traditional ritual music in America, Taiwan and other parts of the globe, very little has been written on the processes and transformations that South Africa’s indigenous ceremonial songs go through over time. This study was prompted by the authors’ interest in, and engagement with the Xhosa initiation song Somagwaza, which has been re-imagined as a popular song, but has also purportedly found its way into other religious spaces. In this article, we attempted to investigate the extent to which the song Somagwaza is still associated with the Xhosa initiation ritual and to analyse evidence of it being decontextualised and secularised in contemporary South Africa. Our methodology included an examination of the various academic treatments of the song, an analysis of the lyrics of a popular song, bearing the same name, holding small focus group discussions, and distributing questionnaires to speakers of isiXhosa on the topic of the song. The data gathered were analysed using the constant comparative method of analysing qualitative research.

Thinning in mature eastern white pine: 43-year case study

2002 ◽  
Vol 78 (4) ◽  
pp. 539-549 ◽  
Author(s):  
Paul D Anderson ◽  
John C Zasada ◽  
Glen W Erickson ◽  
Zigmond A Zasada
Keyword(s):  
Genetic Diversity ◽  
Dna Analysis ◽  
Large Diameter ◽  
White Pine ◽  
Thinning Intensity ◽  
Pine Regeneration ◽  
Volume Production ◽  
Pine Stands ◽  
Over Time

A white pine (Pinus strobus L.) stand at the western margin of the species range, approximately 125 years of age at present, was thinned in 1953 from 33.5 m2 ha-1 to target residual basal areas of 18.4, 23.0, 27.5, and 32.1 m2 ha-1 . Repeated measurement over the following 43-years indicated that the greatest total volume production and the greatest number of large diameter trees occurred in the unit of highest residual density. Over time, the distribution of stems was predominantly random although mortality between 1979 and 1996 resulted in a tendency for clumping in the 23.0 and 27.5 m2 ha-1 treatments. DNA analysis indicated that thinning intensity had little effect on the genetic diversity of residual white pine. This study suggests that mature white pine stands in northern Minnesota may be managed at relatively high densities without loss of productivity. However, regardless of overstory density, there was little or no white pine regeneration occurring in this stand. Key words: thinning, growth, genetic diversity, molecular markers, spatial pattern, regeneration

scholarly journals Analysis of Non-Stationarity for 5.9 GHz Channel in Multiple Vehicle-to-Vehicle Scenarios

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3626
Author(s):  
Fang Li ◽  
Wei Chen ◽  
Yishui Shui
Keyword(s):  
Transmission Rate ◽  
Radio Channel ◽  
Vertical Direction ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Delay Spread ◽  
Important Indicator ◽  
Power Delay Profile ◽  
Channel Characteristics ◽  
Vehicle To Vehicle

The vehicle-to-vehicle (V2V) radio channel is non-stationary due to the rapid movement of vehicles. However, the stationarity of the V2V channels is an important indicator of the V2V channel characteristics. Therefore, we analyzed the non-stationarity of V2V radio channels using the local region of stationarity (LRS). We selected seven scenarios, including three directions of travel, i.e., in the same, vertical, and opposite directions, and different speeds and environments in a similar driving direction. The power delay profile (PDP) and LRS were estimated from the measured channel impulse responses. The results show that the most important influences on the stationary times are the direction and the speed of the vehicles. The average stationary times for driving in the same direction range from 0.3207 to 1.9419 s, the average stationary times for driving in the vertical direction are 0.0359–0.1348 s, and those for driving in the opposite direction are 0.0041–0.0103 s. These results are meaningful for the analysis of the statistical characteristics of the V2V channel, such as the delay spread and Doppler spread. Small-scale fading based on the stationary times affects the quality of signals transmitted in the V2V channel, including the information transmission rate and the information error code rate.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

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