DYNAMICS OF A NONLOCAL DISPERSAL FOOT-AND-MOUTH DISEASE MODEL IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R_(0)is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R_(0)and a principal eigenvalue of an operator L_(0)is built.Moreover,the proposed system exhibits threshold dynamics in terms of R_(0),in the sense that R_(0)determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.

Assessing the effectiveness of the intervention measures of COVID-19 in China based on dynamical method

Normalized interventions were implemented in different cities in China to contain the outbreak of COVID-19 before December 2022.However,the differences in the intensity and timeliness of the implementations lead to differences in final size of the infections.Taking the outbreak of COVID-19 in three representative cities Xi'an,Zhengzhou and Yuzhou in January 2022,as examples,we develop a compartmental model to describe the spread of novel coronavirus and implementation of interventions to assess concretely the effectiveness of Chinese interventions and explore their impact on epidemic patterns.After applying reported human confirmed cases to verify the rationality of the model,we apply the model to speculate transmission trend and length of concealed period at the initial spread phase of the epidemic(they are estimated as 10.5,7.8,8.2 days,respectively),to estimate the range of basic reproduction number(2.9,0.7,1.6),and to define two indexes(transmission rate vt and controlled rate vc)to evaluate the overall effect of the interventions.It is shown that for Zhengzhou,vc is always more than v t with regular interventions,and Xi'an take 8 days to achieve vc>v t twice as long as Yuzhou,which can interpret the fact that the epidemic situation in Xi'an was more severe.By carrying out parameter values,it is concluded that in the early stage,strengthening the precision of close contact tracking and frequency of large-scale nucleic acid testing of non-quarantined population are the most effective on controlling the outbreaks and reducing final size.And,if the close contact tracking strategy is sufficiently implemented,at the late stage largescale nucleic acid testing of non-quarantined population is not essential.

Parameter identifiability of a within-host SARS-CoV-2 epidemic model

Parameter identification involves the estimation of undisclosed parameters within a system based on observed data and mathematical models.In this investigation,we employ DAISY to meticulously examine the structural identifiability of parameters of a within-host SARS-CoV-2 epidemic model,taking into account an array of observable datasets.Furthermore,Monte Carlo simulations are performed to offer a comprehensive practical analysis of model parameters.Lastly,sensitivity analysis is employed to ascertain that decreasing the replication rate of the SARS-CoV-2 virus and curbing the infectious period are the most efficacious measures in alleviating the dissemination of COVID-19 amongst hosts.

COEXISTENCE OF THE STRAINS INDUCED BY MUTATION

In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria （including the disease free equilibrium, dominant equilibria and the coexistence equilibrium） is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.

TWO TYPES OF CONDITION FOR THE GLOBAL STABILITY OF DELAYED SIS EPIDEMIC MODELS WITH NONLINEAR BIRTH RATE AND DISEASE INDUCED DEATH RATE

We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39（4） （1999） 332-352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions BI（N） = be-aN and B3（N） = A/N ＋ c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257（2） （2001） 282-291.

Using the contact network model and Metropolis-Hastings sampling to reconstruct the COVID-19 spread on the “Diamond Princess”

Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.

How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks

In this paper,an extended heterogeneous SIR model is proposed,which generalizes the heterogeneous mean-field theory.Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree,our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates.Then,we analytically study the basic reproductive number and the final epidemic size.Combining with numerical simulations,it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent.If the mean of these two distributions is identical,increasing the variance of susceptibility may block the spread of epidemics,while the corresponding increase in the variance of disease course has little effect on the final epidemic size.It is also shown that positive correlations between individual susceptibility,course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence,whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence.

Optimal control and cost-effective analysis of an agestructured emerging infectious disease model

Emerging infectious diseases are one of the global public health problems which may lead to widespread epidemics and potentially life-threatening infection.Integrated vaccination and physical distancing interventions are two elementary methods for preventing infectious diseases transmission.In this paper,we construct a continuous age-structured model for investigating the transmission dynamics of an emerging infection disease during a short period.We derive the basic regeneration number R 0,the spectral radius of the next generation operator K,which determines the disease outbreak or not.Furthermore,we propose an optimal control problem to take account for the cost-effectiveness of social distancing intervention and vaccination.We rigorously obtain sufficient conditions for a L1 control problem.Numerical simulations show that coupling integrated vaccination and physical distancing intervention could effectively eliminate the infection,and such control strategy is more sensitive for people aged 10e39 and over 60.