This article considers asymptotic stability and stabilization of Markovian jump Boolean networks (MJBNs) with stochastic state-dependent perturbation. By defining an augmented random variable as the ...product of the canonical form of switching signal and state variable, asymptotic stability of an MJBN with perturbation is converted into the set stability of a Markov chain (MC). Then, the concept of induced equations is proposed for an MC, and the corresponding criterion is subsequently derived for asymptotic set stability of an MC by utilizing the solutions of induced equations. This criterion can be, respectively, examined by either a linear programming algorithm or a graphical algorithm. With regards to the stabilization of MJBNs, the time complexity is reduced to a certain extent. Furthermore, all time-optimal signal-based state feedback controllers are designed to stabilize an MJBN towards a given target state. Finally, the feasibility of the obtained results is demonstrated by two illustrative biological examples.
•The novel coronavirus (2019-nCoV) pneumonia has caused 2033 confirmed cases, including 56 deaths in mainland China, by 2020-01-26 17:06.•We aim to estimate the basic reproduction number of 2019-nCoV ...in Wuhan, China using the exponential growth model method.•We estimated that the mean R0 ranges from 2.24 to 3.58 with an 8-fold to 2-fold increase in the reporting rate.•Changes in reporting likely occurred and should be taken into account in the estimation of R0.
An ongoing outbreak of a novel coronavirus (2019-nCoV) pneumonia hit a major city in China, Wuhan, December 2019 and subsequently reached other provinces/regions of China and other countries. We present estimates of the basic reproduction number, R0, of 2019-nCoV in the early phase of the outbreak.
Accounting for the impact of the variations in disease reporting rate, we modelled the epidemic curve of 2019-nCoV cases time series, in mainland China from January 10 to January 24, 2020, through the exponential growth. With the estimated intrinsic growth rate (γ), we estimated R0 by using the serial intervals (SI) of two other well-known coronavirus diseases, MERS and SARS, as approximations for the true unknown SI.
The early outbreak data largely follows the exponential growth. We estimated that the mean R0 ranges from 2.24 (95%CI: 1.96–2.55) to 3.58 (95%CI: 2.89–4.39) associated with 8-fold to 2-fold increase in the reporting rate. We demonstrated that changes in reporting rate substantially affect estimates of R0.
The mean estimate of R0 for the 2019-nCoV ranges from 2.24 to 3.58, and is significantly larger than 1. Our findings indicate the potential of 2019-nCoV to cause outbreaks.
•For the ongoing novel coronavirus disease (CODID-19) outbreak in Wuhan, China, the Chinese government has implemented control measures such as city lockdown to mitigate the impact of the ...epidemic.•We model the outbreak in Wuhan with individual reaction and governmental action (holiday extension, city lockdown, hospitalisation and quarantine) based on some parameters of the 1918 influenza pandemic in London, United Kingdom.•We show the different effects of individual reaction and governmental action and preliminarily estimate the magnitude of these effects.•We also preliminarily estimate the time-varying reporting ratio.
The ongoing coronavirus disease 2019 (COVID-19) outbreak, emerged in Wuhan, China in the end of 2019, has claimed more than 2600 lives as of 24 February 2020 and posed a huge threat to global public health. The Chinese government has implemented control measures including setting up special hospitals and travel restriction to mitigate the spread. We propose conceptual models for the COVID-19 outbreak in Wuhan with the consideration of individual behavioural reaction and governmental actions, e.g., holiday extension, travel restriction, hospitalisation and quarantine. We employe the estimates of these two key components from the 1918 influenza pandemic in London, United Kingdom, incorporated zoonotic introductions and the emigration, and then compute future trends and the reporting ratio. The model is concise in structure, and it successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak.
By employing a nonlocal perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of ...semilinear Kirchhoff equations in the following form
-
a
+
b
∫
R
3
|
∇
u
|
2
Δ
u
+
V
(
x
)
u
=
f
(
u
)
,
x
∈
R
3
,
where
a
,
b
>
0
are constants,
V
∈
C
(
R
3
,
R
)
,
f
∈
C
(
R
,
R
)
. The methodology proposed in the current paper is robust, in the sense that, neither the monotonicity condition on
f
nor the coercivity condition on
V
is required. Our result improves the study made by Deng et al. (J Funct Anal 269:3500–3527, 2015), in the sense that, in the present paper, the nonlinearities include the power-type case
f
(
u
)
=
|
u
|
p
-
2
u
for
p
∈
(
2
,
4
)
, in which case, it remains open in the existing literature whether there exist infinitely many sign-changing solutions to the problem above. Moreover,
energy doubling
is established, namely, the energy of sign-changing solutions is strictly larger than two times that of the ground state solutions for small
b
>
0
.
The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence ...indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number 0 = 2.055 (95% CI: 0.523-6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123-45.73). Our sensitivity analyses indicate that 0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.
During the ongoing COVID-19 pandemic, vaccine shortages occur due to various types of constraints, including interruptions in production/supply, higher-than-expected demands, and a lack of resources ...such as healthcare capacity to administer vaccines. Scientifically informed epidemic models have been utilized as pivotal tools to optimize the immunization programs subject to vaccine shortages. The current paper reviews modelling methods to optimize the allocation strategies of vaccines with differential efficacies by using various model-based outcome measures. The models reviewed in this study are expected to be adopted and extended to make contributions on policy development for disease control under the vaccine shortage scenario.
By extending a mechanistic model for the tick-borne pathogen systemic transmission with the consideration of seasonal climate impacts, host movement as well as the co-feeding transmission route, this ...paper proposes a novel modeling framework for describing the spatial dynamics of tick-borne diseases. The net reproduction number for tick growth and basic reproduction number for disease transmission are derived, which predict the global dynamics of tick population growth and disease transmission. Numerical simulations not only verify the analytical results, but also characterize the contribution of co-feeding transmission route on disease prevalence in a habitat and the effect of host movement on the spatial spreading of the pathogen.
•As of March 1, 2020, Iran had reported 987 COVID-19 cases, including 54 associated deaths.•At least six neighboring countries (Bahrain, Iraq, Kuwait, Oman, Afghanistan, and Pakistan) had reported ...imported COVID-19 cases from Iran.•We estimated that 16 533 (95% confidence interval 5925–35 538) COVID-19 cases had occurred in Iran by February 25, 2020.•Iran’s ascertainment rate could have been at a level of 0.6% on February 25, 2020.
As of March 1, 2020, Iran had reported 987 novel coronavirus disease (COVID-19) cases, including 54 associated deaths. At least six neighboring countries (Bahrain, Iraq, Kuwait, Oman, Afghanistan, and Pakistan) had reported imported COVID-19 cases from Iran. In this study, air travel data and the numbers of cases from Iran imported into other Middle Eastern countries were used to estimate the number of COVID-19 cases in Iran. It was estimated that the total number of cases in Iran was 16 533 (95% confidence interval: 5925–35 538) by February 25, 2020, before the UAE and other Gulf Cooperation Council countries suspended inbound and outbound flights from Iran.
In December 2019, an outbreak of respiratory illness caused by a novel coronavirus (2019-nCoV) emerged in Wuhan, China and has swiftly spread to other parts of China and a number of foreign ...countries. The 2019-nCoV cases might have been under-reported roughly from 1 to 15 January 2020, and thus we estimated the number of unreported cases and the basic reproduction number,
, of 2019-nCoV.
We modelled the epidemic curve of 2019-nCoV cases, in mainland China from 1 December 2019 to 24 January 2020 through the exponential growth. The number of unreported cases was determined by the maximum likelihood estimation. We used the serial intervals (SI) of infection caused by two other well-known coronaviruses (CoV), Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) CoVs, as approximations of the unknown SI for 2019-nCoV to estimate
.
We confirmed that the initial growth phase followed an exponential growth pattern. The under-reporting was likely to have resulted in 469 (95% CI: 403-540) unreported cases from 1 to 15 January 2020. The reporting rate after 17 January 2020 was likely to have increased 21-fold (95% CI: 18-25) in comparison to the situation from 1 to 17 January 2020 on average. We estimated the
of 2019-nCoV at 2.56 (95% CI: 2.49-2.63).
The under-reporting was likely to have occurred during the first half of January 2020 and should be considered in future investigation.
Several safe and effective vaccines are available to prevent individuals from experiencing severe illness or death as a result of COVID-19. Widespread vaccination is widely regarded as a critical ...tool in the fight against the disease. However, some individuals may choose not to vaccinate due to vaccine hesitancy or other medical conditions. In some sectors, regular compulsory testing is required for such unvaccinated individuals. Interestingly, different sectors require testing at various frequencies, such as weekly or biweekly. As a result, it is essential to determine the optimal testing frequency and identify underlying factors. This study proposes a population-based model that can accommodate different personal decision choices, such as getting vaccinated or undergoing regular tests, as well as vaccine efficacies and uncertainties in epidemic transmission. The model, formulated as impulsive differential equations, uses time instants to represent the reporting date for the test result of an unvaccinated individual. By employing well-accepted indices to measure transmission risk, including the basic reproduction number, the peak time, the final size, and the number of severe infections, the study shows that an optimal testing frequency is highly sensitive to parameters involved in the transmission process, such as vaccine efficacy, disease transmission rate, test accuracy, and existing vaccination coverage. The testing frequency should be appropriately designed with the consideration of all these factors, as well as the control objectives measured by epidemiological quantities of great concern.
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