Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate

A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibria of the model is obtained with respect to the basic reproduction number R_(0).Specifically,it shows that the disease-free equilibrium E^(0)is globally asymptotically stable(GAS)for R_(0)<1,and globally attractive(GA)for R_(0)=1,while the endemic equilibrium E^(*)is GAS and E^(0)is unstable for R_(0)>1.Especially,to obtain the global stability of the equilibrium E^(*)for R_(0)>1,the weak persistence of the model is proved by some analysis techniques.

A mathematical model for simulating the phase-based transmissibility of a novel coronavirus

Background:As reported by the World Health Organization,a novel coronavirus(2019-nCoV)was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January,2020.The virus was named as severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)by International Committee on Taxonomy of Viruses on 11 February,2020.This study aimed to develop a mathematical model for calculating the transmissibility of the virus.Methods:In this study,we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source(probably be bats)to the human infection.Since the Bats-HostsReservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market(reservoir)to people,we simplified the model as Reservoir-People(RP)transmission network model.The next generation matrix approach was adopted to calculate the basic reproduction number(R0)from the RP model to assess the transmissibility of the SARS-CoV-2.Results:The value of R0 was estimated of 2.30 from reservoir to person and 3.58 from person to person which means that the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population was 3.58.Conclusions:Our model showed that the transmissibility of SARS-CoV-2 was higher than the Middle East respiratory syndrome in the Middle East countries,similar to severe acute respiratory syndrome,but lower than MERS in the Republic of Korea.

Risk estimation and prediction of the transmission of coronavirus disease-2019(COVID-19)in the mainland of China excluding Hubei province

Background In December 2019,an outbreak of coronavirus disease(later named as COVID-19)was identified in Wuhan,China and,later on,detected in other parts of China.Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures,estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model.Methods A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed.COVID-19 daily data of the mainland of China excluding Hubei province,including the cumulative confirmed cases,the cumulative deaths,newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020,were archived from the National Health Commission of China(NHCC).We parameterize the model by using the Markov Chain Monte Carlo(MCMC)method and estimate the control reproduction number(Rc),as well as the effective daily reproduction ratio-Re(t),of the disease transmission in the mainland of China excluding Hubei province.Results The estimation outcomes indicate that Rc is 3.36(95%CI:3.20–3.64)and Re(t)has dropped below 1 since 31 January 2020,which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission.Moreover,our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected,and may even cause a second wave of epidemic or outbreaks.By calculating the effective reproduction ratio,we prove that the contact rate should be kept at least less than 30%of the normal level by April,2020.Conclusions To ensure the pandemic ending rapidly,it is necessary to maintain the current integrated restrict interventions and self-protection measures,including travel restriction,quarantine of entry,contact tracing followed by quarantine and isolation and reduction of contact,like wearing masks,keeping social distance,etc.People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April.If all the above conditions are met,the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.

A five-compartment model of age-specific transmissibility of SARS-CoV-2

Background:The novel coronavirus,severe acute respiratory syndrome coronavirus 2(SARS-CoV-2,also called 2019-nCoV)causes different morbidity risks to individuals in different age groups.This study attempts to quantify the age-specific transmissibility using a mathematical model.Methods:An epidemiological model with five compartments(susceptible-exposed-symptomatic-asymptomatic-recovered/removed[SEIAR])was developed based on observed transmission features.Coronavirus disease 2019(COVID-19)cases were divided into four age groups:group 1,those≤14years old;group 2,those 15 to 44years old;group 3,those 45 to 64years old;and group 4,those≥65 years old.The model was initially based on cases(including imported cases and secondary cases)collected in Hunan Province from January 5 to February 19,2020.Another dataset,from Jilin Province,was used to test the model.Results:The age-specific SEIAR model fitted the data well in each age group(P<0.001).In Hunan Province,the highest transmissibility was from age group 4 to 3(median:β43=7.71×10-9;SAR43=3.86×10-8),followed by group 3 to 4(median:β34=3.07×10-9;SAR34=1.53×10-8),group 2 to 2(median:β22=1.24×10-9;SAR22=6.21×10-9),and group 3 to 1(median:β31=4.10×10-10;SAR31=2.08×10-9).The lowest transmissibility was from age group 3 to 3(median:β33=1.64×10-19;SAR33=8.19×10-19),followed by group 4 to 4(median:β44=3.66×10-17;SAR44=1.83×10-16),group 3 to 2(median:β32=1.21×10-16;SAR32=6.06×10-16),and group 1 to 4(median:β14=7.20×10-14;SAR14=3.60×10-13).In Jilin Province,the highest transmissibility occurred from age group 4 to 4(median:β43=4.27×10-8;SAR43=2.13×10-7),followed by group 3 to 4(median:β34=1.81×10-8;SAR34=9.03×10-8).Conclusions:SARS-CoV-2 exhibits high transmissibility between middle-aged(45 to 64 years old)and elderly(≥65 years old)people.Children(≤14 years old)have very low susceptibility to COVID-19.This study will improve our understanding of the transmission feature of SARS-CoV-2 in different age groups and suggest the most prevention measures should be applied to middle-aged and elderly people.

Shigellosis seasonality and transmission characteristics in different areas of China: A modelling study

Objective:In China,the burden of shigellosis is unevenly distributed,notably across various ages and geographical areas.Shigellosis temporal trends appear to be seasonal.We should clarify seasonal warnings and regional transmission patterns.Method:This study adopted a Logistic model to assess the seasonality and a dynamics model to compare the transmission in different areas.The next-generation matrix was used to calculate the effective reproduction number(Reff)to quantify the transmissibility.Results:In China,the rate of shigellosis fell from 35.12 cases per 100,000 people in 2005 to 7.85 cases per 100,000 people in 2017,peaking in June and August.After simulation by the Logistic model,the‘peak time’is mainly concentrated from mid-June to mid-July.China's‘early warning time’is primarily focused on from April to May.We predict the‘peak time’of shigellosis is the 6.30th month and the‘early warning time’is 3.87th month in 2021.According to the dynamics model results,the water/food transfer pathway has been mostly blocked off.The transmissibility of different regions varies greatly,such as the mean Reff of Longde County(3.76)is higher than Xiamen City(3.15),higher than Chuxiong City(2.52),and higher than Yichang City(1.70).Conclusion:The‘early warning time’for shigellosis in China is from April to May every year,and it may continue to advance in the future,such as the early warning time in 2021 is in mid-March.Furthermore,we should focus on preventing and controlling the personto-person route of shigellosis and stratified deploy prevention and control measures according to the regional transmission.