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Hepatitis B is an infectious disease worthy of attention. Considering the incubation period, psychological inhibition factor, vaccine, limited medical resources and horizontal transmission, an SIRS model is proposed to describe hepatitis B transmission dynamics. In order to describe the behavior changes caused by people's psychological changes, the non-monotonic incidence rate is adopted in the model. We use the saturated treatment rate to describe the limited medical resources. Mathematical analysis shows the existence conditions of the equilibria, forward or backward bifurcation, Hopf bifurcation and the Bogdanov–Takens bifurcation. During the observation of the case data of hepatitis B in China, it is found that there are mainly three features, periodic outbreaks, aperiodic outbreaks, and periodic outbreaks turns to aperiodic outbreaks. According to the above features, we select three different representative regions, Jiangxi, Zhejiang province and Beijing, and then use our model to fit the actual monthly hepatitis B case data. The basic reproduction numbers that we estimated are 1.7712, 1.4805 and 1.4132, respectively. The results of data fitting are consistent with those of theoretical analysis. According to the sensitivity analysis of ℛ 0 , we conclude that reducing contact, increasing treatment rate, strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B. [ABSTRACT FROM AUTHOR]

Malaria is one of the most common mosquito-borne diseases in the world. To understand the joint effects of the vector-bias, seasonality, spatial heterogeneity multi-strain and the extrinsic incubation period of the parasite on the dynamics of malaria, we formulate a time-periodic two-strain malaria reaction–diffusion model with delay and nonlocal terms. We then consider threshold conditions that determine whether malaria will spread. More specifically, the basic reproduction number R i for single strain-i and invasion number R ^ i for each strain- i (i = 1 , 2) are derived. Our results imply that if max { R 1 , R 2 } < 1 , then the disease-free periodic solution is globally attractive; if R i > 1 > R j (i , j = 1 , 2 , i ≠ j) , then competitive exclusion, where the jth strain dies out and the ith strain persists; if min { R ^ 1 , R ^ 2 , R 1 , R 2 } > 1 , then the disease persists. Our numerical simulations show that spatially heterogeneous infection can increase the basic reproduction number and the omission of the vector-bias effect will underestimate the infection risk of the disease. [ABSTRACT FROM AUTHOR]

Brucellosis is a major worldwide problem in public health. In this paper, we established and analyzed the Susceptible-Exposed-Infectious-Vaccinated for small ruminant–Susceptible-Exposed-Infectious-Vaccinated for cattle–Susceptible-Infectious-Recovered for human (SEIV–SEIV–SIR) model of Brucellosis with an incubation period which considered that human was infected through direct contact with infected humans, infected small ruminant, infected cattle and indirect contact with Brucella in the environment. The basic reproduction number R 0 of the model is computed by the spectral radius of the next-generation matrix. We proved that the disease-free equilibrium exists and we analyzed that the disease-free equilibrium point and endemic equilibrium point are global stability by constructing the L y a p u n o v function and applying the L a s a l l e invariant principle. Numerical solutions and analytical reveal that the prevention and control measures for Brucella should be to detect infected livestock in time, reduce contact with infected livestock and increase the cure rate of infected humans. [ABSTRACT FROM AUTHOR]

The incubation period and generation time are key characteristics in the analysis of infectious diseases. The commonly used contact‐tracing–based estimation of incubation distribution is highly influenced by the individuals' judgment on the possible date of exposure, and might lead to significant errors. On the other hand, interval censoring–based methods are able to utilize a much larger set of traveling data but may encounter biased sampling problems. The distribution of generation time is usually approximated by observed serial intervals. However, it may result in a biased estimation of generation time, especially when the disease is infectious during incubation. In this paper, the theory from renewal process is partially adopted by considering the incubation period as the interarrival time, and the duration between departure from Wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals. In addition, a consistent estimator for the distribution of generation time based on incubation period and serial interval is proposed for incubation‐infectious diseases. A real case application to the current outbreak of COVID‐19 is implemented. We find that the incubation period has a median of 8.50 days (95% confidence interval [CI] [7.22; 9.15]). The basic reproduction number in the early phase of COVID‐19 outbreak based on the proposed generation time estimation is estimated to be 2.96 (95% CI [2.15; 3.86]). [ABSTRACT FROM AUTHOR]

The article presents the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries and robust inferences could bemade. Topics include the impact of physical distancing interventions was typically not seen after implementation, and the temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number for initiating interventions.

Background: As of June 8, 2020, the global reported number of COVID-19 cases had reached more than 7 million with over 400 000 deaths. The household transmissibility of the causative pathogen, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), remains unclear. We aimed to estimate the secondary attack rate of SARS-CoV-2 among household and non-household close contacts in Guangzhou, China, using a statistical transmission model.Methods: In this retrospective cohort study, we used a comprehensive contact tracing dataset from the Guangzhou Center for Disease Control and Prevention to estimate the secondary attack rate of COVID-19 (defined as the probability that an infected individual will transmit the disease to a susceptible individual) among household and non-household contacts, using a statistical transmission model. We considered two alternative definitions of household contacts in the analysis: individuals who were either family members or close relatives, such as parents and parents-in-law, regardless of residential address, and individuals living at the same address regardless of relationship. We assessed the demographic determinants of transmissibility and the infectivity of COVID-19 cases during their incubation period.Findings: Between Jan 7, 2020, and Feb 18, 2020, we traced 195 unrelated close contact groups (215 primary cases, 134 secondary or tertiary cases, and 1964 uninfected close contacts). By identifying households from these groups, assuming a mean incubation period of 5 days, a maximum infectious period of 13 days, and no case isolation, the estimated secondary attack rate among household contacts was 12·4% (95% CI 9·8-15·4) when household contacts were defined on the basis of close relatives and 17·1% (13·3-21·8) when household contacts were defined on the basis of residential address. Compared with the oldest age group (≥60 years), the risk of household infection was lower in the youngest age group (<20 years; odds ratio [OR] 0·23 [95% CI 0·11-0·46]) and among adults aged 20-59 years (OR 0·64 [95% CI 0·43-0·97]). Our results suggest greater infectivity during the incubation period than during the symptomatic period, although differences were not statistically significant (OR 0·61 [95% CI 0·27-1·38]). The estimated local reproductive number (R) based on observed contact frequencies of primary cases was 0·5 (95% CI 0·41-0·62) in Guangzhou. The projected local R, had there been no isolation of cases or quarantine of their contacts, was 0·6 (95% CI 0·49-0·74) when household was defined on the basis of close relatives.Interpretation: SARS-CoV-2 is more transmissible in households than SARS-CoV and Middle East respiratory syndrome coronavirus. Older individuals (aged ≥60 years) are the most susceptible to household transmission of SARS-CoV-2. In addition to case finding and isolation, timely tracing and quarantine of close contacts should be implemented to prevent onward transmission during the viral incubation period.Funding: US National Institutes of Health, Science and Technology Plan Project of Guangzhou, Project for Key Medicine Discipline Construction of Guangzhou Municipality, Key Research and Development Program of China. [ABSTRACT FROM AUTHOR]

Background: With the spread of SARS-CoV-2 worldwide, understanding the basic epidemiological parameter values of COVID-19 from real-world data in mega-cities is essential for disease prevention and control.Methods: To investigate the epidemiological parameters in SARS-CoV-2 infected cases in Beijing, we studied all confirmed cases and close contacts in Beijing from Jan 1st to Apr 3rd 2020. The epidemiological and virological characteristics of SARS-CoV-2 were analyzed.Results: A total of 602 cases were positive for SARS-CoV-2, including 585 confirmed patients and 17 asymptomatic infections. The imported cases were mainly from Wuhan initially and then from abroad. Among 585 confirmed case-patients, the median age was 39 years old. The mean incubation period was 6.3 days. The secondary attack rate among households was higher than social contacts (15.6 vs 4.6%). The secondary attack rate of healthcare workers (HCWs) was higher than non-HCWs' (7.3 vs 4.2%). The basic reproduction number was 2.0, and the average serial interval was 7.6 days. No significant genetic variant was identified.Conclusions: The transmissibility of SARS-CoV-2 was relatively high, especially among households and from HCWs, which draws specific public health attention. So far, no evidence of widespread circulation of SARS-CoV-2 in communities in Beijing was found. [ABSTRACT FROM AUTHOR]

We propose a diffusive viral model incorporating cell‐to‐cell infection mode, nonlinear incidences, incubation period, and spatial heterogeneity. For the spatially heterogeneous model, we derive the extinction/persistence result by the basic reproduction number R0. For the spatially homogeneous model, we study global stabilities of steady states by establishing Lyapunov functions. The existing method for studying global stabilities of diffusive viral models has been generalized, which weakens the required conditions. Some existing results can be covered and improved. A specific example is given to illustrate the general results. In addition, we show that R0 is underestimated if we neglect incubation period of infected cells. [ABSTRACT FROM AUTHOR]

Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number R0 $\mathcal{R}_0$ R 0 (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If R0 > 1 $\mathcal{R}_0 >1$ R 0 > 1 , then the number of latently infected individuals exponentially grows. However, if R0 < 1 $\mathcal{R}_0 R 0 < 1 (e.g. due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth-decays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed. [ABSTRACT FROM AUTHOR]

Modern society has not forgotten yet epidemics that killed millions in the last millennium and the COVID-19 pandemic caused by the SARS CoV-2 has recently emerged. With the onset of the Wuhan epidemic in the Chinese province of Hubei, the initially called new corona virus due to the similarity of 80 % to the 2002 SARS virus was renamed to SARS CoV-2. The virus was originally isolated from bronchoalveolar aspirate specimens. Viral RNK was detected in 6 of 41 blood samples with clinical signs of infection. A senior Chinese expert told to the media that the median incubation period was 7 days, ranging from 2 -1 2. The International Health Regulations Emergency Committee for Epidemics gives a preliminary estimate basic reproduction number R0 of 1.4 - 2.5. COVID-19 is mainly transmitted by close contact with the infected by drops due to sneezing and coughing. Fever, cough, myalgia and fatigue are the predominant initial signs and symptoms. The clinical picture is non-specific. Exacerbation occurs suddenly, as bilateral interstitial pneumonia that requires admission to intensive care. Initial lethality in hospitalised cases was 15 %, but these estimates had to be taken with reserve as the situation evolved. According to recent data, the global fatality rate is 3.7 %, the lethality rate in China is 3.9 % and in Italy 6.8 %. According to data from the Chinese Centre for Disease Control and Prevention, of 44,672 confirmed cases 1,023 people died, therefore lethality was 2.3 %. In the absence of specific prevention and control measures, mankind is limited to general prevention measures. [ABSTRACT FROM AUTHOR]

Seasonal change has played a critical role in the evolution dynamics of West Nile virus transmission. In this paper, we formulate and analyze a novel delay differential equation model, which incorporates seasonality, the vertical transmission of the virus, the temperature-dependent maturation delay and the temperature-dependent extrinsic incubation period in mosquitoes. We first introduce the basic reproduction ratio R 0 for this model and then show that the disease is uniformly persistent if R 0 > 1 . It is also shown that the disease-free periodic solution is attractive if R 0 < 1 , provided that there is only a small invasion. In the case where all coefficients are constants and the disease-induced death rate of birds is zero, we establish a threshold result on the global attractivity in terms of R 0 . Numerically, we study the West Nile virus transmission in Orange County, California, USA. [ABSTRACT FROM AUTHOR]

West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and seasonality on the transmission of WNv, we develop a delay differential system with stage-structure and time-varying delays. We then derive the mosquito reproduction number R0V and basic reproduction number R0 and show that these two numbers serve as threshold parameters that determine whether WNv will spread. As an application, we conduct a case study for WNv transmission in Los Angeles County, California. We also carry out numerical simulations to identify the situations that require time-periodic delays. Moreover, we find that rising temperatures may potentially increase the risk of disease outbreaks. [ABSTRACT FROM AUTHOR]

Background: Zika virus (ZIKV) is transfusion-transmissible. In Australia the primary vector, Aedes aegypti, is established in the north-east, such that local transmission is possible following importation of an index case, which has the potential to impact on blood transfusion safety and public health. We estimated the basic reproduction number (R 0 ) to model the epidemic potential of ZIKV in Australian locations, compared this with the ecologically similar dengue viruses (DENV), and examined possible implications for blood transfusion safety.Study Design and Methods: Varying estimates of vector control efficiency and extrinsic incubation period, "best-case" and "worst-case" scenarios of monthly R 0 for ZIKV and DENV were modeled from 1996 to 2015 in 11 areas. We visualized the geographical distribution of blood donors in relation to areas with epidemic potential for ZIKV.Results: Epidemic potential (R 0 > 1) existed for ZIKV and DENV throughout the study period in a number of locations in northern Australia (Cairns, Darwin, Rockhampton, Thursday Island, Townsville, and Brisbane) during the warmer months of the year. R 0 for DENV was greater than ZIKV and was broadly consistent with annual estimates in Cairns. Increased vector control efficiency markedly reduced the epidemic potential and shortened the season of local transmission. Australian locations that provide the greatest number of blood donors did not have epidemic potential for ZIKV.Conclusion: We estimate that areas of north-eastern Australia could sustain local transmission of ZIKV. This early contribution to understanding the epidemic potential of ZIKV may assist in the assessment and management of threats to blood transfusion safety. [ABSTRACT FROM AUTHOR]

A family of deterministic SEIRS epidemic dynamic models for malaria is presented. The family type is determined by a general functional response for the nonlinear incidence rate of the disease. Furthermore, the malaria models exhibit three random delays — the incubation periods of the plasmodium inside the female mosquito and human hosts, and also the period of effective acquired natural immunity against the disease. Insights about the effects of the delays and the nonlinear incidence rate of the disease on (1) eradication and (2) persistence of malaria in the human population are obtained via analyzing and interpreting the global asymptotic stability results of the disease-free and endemic equilibrium of the system. The basic reproduction numbers and other threshold values for malaria are calculated, and superior threshold conditions for the stability of the equilibria are found. Numerical simulation results are presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a time-periodic reaction-diffusion model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. The basic reproduction number R0 is derived, and it is shown that the disease-free periodic solution is globally attractive if R0<1, while there is an endemic periodic solution and the disease is uniformly persistent if R0>1. Numerical simulations indicate that prolonging the EIP may be helpful in the disease control, while spatial heterogeneity of the disease transmission coefficient may increase the disease burden. [ABSTRACT FROM AUTHOR]

Bat-borne rabies is a viral infection caused by lyssaviruses. To explore the complex interaction between bats and cattle, we develop a periodic compartment system with seasonality, temperature-dependent incubation period and different control measures. We derive the basic reproduction number R 0 and show it determines the global dynamics. In particular, we prove the non-existence of positive periodic solutions in the critical case where R 0 = 1. Numerically, we observe that sufficient long time-varying incubation periods could potentially increase the disease outbreak risk. [ABSTRACT FROM AUTHOR]

Mathematical modeling and notably the basic reproduction number R0 have become popular tools for the description of vector-borne disease dynamics. We compare two widely used methods to calculate the probability of a vector to survive the extrinsic incubation period. The two methods are based on different assumptions for the duration of the extrinsic incubation period; one method assumes a fixed period and the other method assumes a fixed daily rate of becoming infectious. We conclude that the outcomes differ substantially between the methods when the average life span of the vector is short compared to the extrinsic incubation period. [ABSTRACT FROM AUTHOR]

• The mean incubation period is 2-14 days, and the basic reproduction number is 2.24-3.58. • COVID-19 infection should be diagnosed clinically with typical respiratory syndromes coupled with recent exposure. • Chest computerized tomography (CT) could facilitate early diagnosis. • Public health measures, such as isolation, quarantine, social distancing and community containment, can curb COVID-19. • Clinical trials assessing antivirals, chloroquine, hydroxychloroquine, glucocorticoids, convalescent plasma transfusion against COVID-19. In December 2019, the outbreak of the novel coronavirus disease (COVID-19) in China spread worldwide, becoming an emergency of major international concern. SARS-CoV-2 infection causes clusters of severe respiratory illness similar to severe acute respiratory syndrome coronavirus. Human-to-human transmission via droplets, contaminated hands or surfaces has been described, with incubation times of 2-14 days. Early diagnosis, quarantine, and supportive treatments are essential to cure patients. This paper reviews the literature on all available information about the epidemiology, diagnosis, isolation and treatments of COVID-19. Treatments, including antiviral agents, chloroquine and hydroxychloroquine, corticosteroids, antibodies, convalescent plasma transfusion and vaccines, are discussed in this article. In addition, registered trials investigating treatment options for COVID-19 infection are listed. [ABSTRACT FROM AUTHOR]

As the novel coronavirus (SARS-CoV-2) continues to spread rapidly across the globe, we aimed to identify and summarize the existing evidence on epidemiological characteristics of SARS-CoV-2 and the effectiveness of control measures to inform policymakers and leaders in formulating management guidelines, and to provide directions for future research. We conducted a systematic review of the published literature and preprints on the coronavirus disease (COVID-19) outbreak following predefined eligibility criteria. Of 317 research articles generated from our initial search on PubMed and preprint archives on 21 February 2020, 41 met our inclusion criteria and were included in the review. Current evidence suggests that it takes about 3-7 days for the epidemic to double in size. Of 21 estimates for the basic reproduction number ranging from 1.9 to 6.5, 13 were between 2.0 and 3.0. The incubation period was estimated to be 4-6 days, whereas the serial interval was estimated to be 4-8 days. Though the true case fatality risk is yet unknown, current model-based estimates ranged from 0.3% to 1.4% for outside China. There is an urgent need for rigorous research focusing on the mitigation efforts to minimize the impact on society. [ABSTRACT FROM AUTHOR]

Malaria is the world's most prevalent mosquito-borne disease caused by Plasmodium parasites, and responsible for over half a million deaths per year. To understand the effects of the intrinsic and extrinsic incubation periods of the parasite within the humans and mosquitoes, respectively, and the seasonality on disease transmission, we propose a periodic malaria model with delays. The basic reproduction number R 0 is derived, and it is shown that R 0 is a threshold parameter between the extinction and persistence of the disease. In the case where all the coefficients are constants and the intrinsic incubation period is ignored, we also prove the global attractivity of the endemic equilibrium when R 0 > 1. Numerical simulations indicate that prolonging the incubation period in mosquitoes is more effective than prolonging the incubation period in humans for disease control. It is also found that increasing the strength of seasonal forcing will lead to a higher epidemic peak. • A periodic malaria model with two delays is proposed, one delay describing the EIP and the other representing the IIP. • The definition and numerical estimation of the basic reproduction number R 0 are given. • The threshold dynamics of the model in terms of R 0 is studied. • Exploring the influences of seasonality, the EIP and IIP on the disease transmission. [ABSTRACT FROM AUTHOR]

• Emergence of 2019 novel coronavirus (2019-nCoV) in China has caused a large global outbreak and major public health issue. • At 9 February 2020, data from the WHO has shown >37 000 confirmed cases in 28 countries (>99% of cases detected in China). • 2019-nCoV is spread by human-to-human transmission via droplets or direct contact. • Infection estimated to have an incubation period of 2–14 days and a basic reproduction number of 2.24–3.58. • Controlling infection to prevent spread of the 2019-nCoV is the primary intervention being used. The emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; previously provisionally named 2019 novel coronavirus or 2019-nCoV) disease (COVID-19) in China at the end of 2019 has caused a large global outbreak and is a major public health issue. As of 11 February 2020, data from the World Health Organization (WHO) have shown that more than 43 000 confirmed cases have been identified in 28 countries/regions, with >99% of cases being detected in China. On 30 January 2020, the WHO declared COVID-19 as the sixth public health emergency of international concern. SARS-CoV-2 is closely related to two bat-derived severe acute respiratory syndrome-like coronaviruses, bat-SL-CoVZC45 and bat-SL-CoVZXC21. It is spread by human-to-human transmission via droplets or direct contact, and infection has been estimated to have mean incubation period of 6.4 days and a basic reproduction number of 2.24–3.58. Among patients with pneumonia caused by SARS-CoV-2 (novel coronavirus pneumonia or Wuhan pneumonia), fever was the most common symptom, followed by cough. Bilateral lung involvement with ground-glass opacity was the most common finding from computed tomography images of the chest. The one case of SARS-CoV-2 pneumonia in the USA is responding well to remdesivir, which is now undergoing a clinical trial in China. Currently, controlling infection to prevent the spread of SARS-CoV-2 is the primary intervention being used. However, public health authorities should keep monitoring the situation closely, as the more we can learn about this novel virus and its associated outbreak, the better we can respond. [ABSTRACT FROM AUTHOR]

In this work, we have developed a Coxian-distributed SEIR model when incorporating an empirical incubation period. We show that the global dynamics are completely determined by a basic reproduction number. An application of the Coxian-distributed SEIR model using data of an empirical incubation period is explored. The model may be useful for resolving the realistic intrinsic parts in classical epidemic models since Coxian distribution approximately converges to any distribution. [ABSTRACT FROM AUTHOR]