Non-local Infection Research Articles

On cognitive epidemic models: spatial segregation versus nonpharmaceutical interventions.

Fick's law and the Fokker-Planck law of diffusion are applied to manifest the cognitive dispersal of individuals in two reaction-diffusion SEIR epidemic models, where the disease transmission is illustrated by nonlocal infection mechanisms in heterogeneous environments. Building upon the well-posedness of solutions, threshold dynamics are discussed in terms of the basic reproduction numbers for the two cognitive epidemic models. The numerical investigation reveals that the Fokker-Planck law can better describe the diffusion of individuals by taking different dispersal strategies of exposed individuals in our cognitive epidemic models, and provides some insights on spatial segregation and nonpharmaceutical interventions: (i) spatial segregation occurs in the random diffusion model when the nonlocal infection radius is small, while it appears in the symmetric diffusion model when the radius is large; (ii) nonpharmaceutical interventions on restricting the dispersal of exposed and infected individuals do not contribute to reducing the infection proportion, but rather eliminate the disease in a region, which expands as the nonlocal infection radius increases. We additionally find that the final infection size in the random diffusion model is significantly smaller than that in the symmetric diffusion model and decreases as the nonlocal infection radius increases.

Diversification, vertical integration and economic resilience: evidence from intercity truck flows during COVID-19 in China

Abstract This article examines economic resilience by combining high-frequency truck flows and the lockdown policy shock during COVID-19 in China. We discover that the truck flows in regions with higher levels of diversification and vertical integration see a smaller decrease in response to the COVID-19 shock. Dynamically, such moderating effects of diversification and vertical integration get smaller with the recovery of interregional economic linkages. Diversification and integration also mitigate the negative impact from nonlocal infection cases. The association between the industrial structure attributes and economic resilience is more prominent in regions with lower centrality in the nationwide intercity truck flow network.

Temporal-spatial analysis of a foot-and-mouth disease model with spatial diffusion and vaccination.

Foot-and-mouth disease is an acute, highly infectious, and economically significant transboundary animal disease. Vaccination is an efficient and cost-effective measure to prevent the transmission of this disease. The primary way that foot-and-mouth disease spreads is through direct contact with infected animals, although it can also spread through contact with contaminated environments. This paper uses a diffuse foot-and-mouth disease model to account for the efficacy of vaccination in managing the disease. First, we transform an age-space structured foot-and-mouth disease into a diffusive epidemic model with nonlocal infection coupling the latent period and the latent diffusive rate. The basic reproduction number, which determines the outbreak of the disease, is then explicitly formulated. Finally, numerical simulations demonstrate that increasing vaccine efficacy has a remarkable effect than increasing vaccine coverage.

An SIR epidemic model with nonlocal diffusion, nonlocal infection and free boundaries

In this paper, taking into account the long range dispersal, environmental carrying capacity and propagation of viruses in the air, we propose a new SIR epidemic model with nonlocal diffusion, nonlocal infection and free boundaries. We first prove that such a nonlocal problem with free boundaries has a unique global solution. Then find the basic reproduction number R0(θ/b,(−h0,h0)) and show that when R0(θ/b,(−h0,h0))≥1 the disease will spread; when R0(θ/b,(−h0,h0))<1, the disease will spread or not depending on the expanding ability μ of I. Moreover, we give the conditions that determine R0(θ/b,(−h0,h0))=(>,<)1, and give the criteria for spreading and vanishing.

On the Dynamics of a Diffusive Foot-and-Mouth Disease Model with Nonlocal Infections

On the Dynamics of a Diffusive Foot-and-Mouth Disease Model with Nonlocal Infections

Diffusive host-pathogen model revisited: Nonlocal infections, incubation period and spatial heterogeneity

We formulate and analyze a general diffusive host-pathogen model with an incubation period and nonlocal infections in a spatially heterogeneous environment. The model system is partially degenerate and the solution map is not compact. We first prove that the solutions of the model exist globally and are ultimately bounded. Next, we define the basic reproduction number R0 as the spectral radius of the sum of two next generation operators corresponding to direct and indirect infection modes, and prove that R0 is decreasing with respect to the incubation period and the diffusion coefficient of infectious hosts under some conditions. Finally, we demonstrate that the model system possesses a global attractor, and explore the global dynamics of the system. Especially, we show that the infection-free steady state is globally asymptotically stable if R0≤1. On the other hand, if R0>1, then the infection will persist and the model system admits at least one positive steady state. For spatial homogeneous system, global asymptotic stability of the positive steady state is proved via Lyapunov functional technique. Numerical simulation is conducted to explore singular perturbation phenomenon when the diffusion coefficients approach zero. We observe that the diffusion will not only spread the infection to the low-risk region, but it may also increase the infection level in the high-risk region.

Dynamical analysis of a nonlocal delayed and diffusive HIV latent infection model with spatial heterogeneity

To study the impact of two time delays (latency period caused by HIV latency infected cell and viral production period caused by HIV infected cell) on the HIV infection processes in heterogenous environment, an HIV latent infection model with spatial diffusion and non-local infections is derived and investigated in this paper. Applying the definition of the next reproduction operator, we obtain the basic reproduction number R0, which is a threshold value for determining whether the breakout of HIV infection or not. More precisely, the infection-free equilibrium is globally attractive if R0<1 and the infection is uniformly persistent if R0>1. In particular, an explicit formula of R˜0 is obtained in the homogeneous case and the global dynamics of the homogeneous case are also analyzed. The influences of time delays, HAART treatment and infection heterogeneity on HIV infections are discussed via numerical simulations. This work reveals that the use of the spatially averaged parameters may underestimate HIV infection. Therefore, the spatial heterogeneity is a key factor that cannot be ignored when clinical medical staff design the treatment strategies for HIV infection.

Dynamics of a seasonal brucellosis disease model with nonlocal transmission and spatial diffusion

Brucellosis has been increasingly concerned with the animal health and a huge loss of economics. Multiple transmission routes, seasonal pattern and spatial diffusion have been identified in brucellosis propagations. Meanwhile, infectious ability strongly depends on the distance of each adjacent infectious individual. Such property can be captured by a nonlocal infection with some integrable functions. In this paper, we first propose a seasonal brucellosis epidemic model with nonlocal transmissions and spatial diffusions. We calculate the next generation operator R(x) by a renewal process. The basic reproduction number R0 is defined as the spectral radius of R(x), which plays an equivalent role in a principal eigenvalue of a linear operator. It is shown that the proposed model exhibits the threshold dynamics in terms of R0, i.e, if R0<1, then the brucella-free steady state is globally asymptotically stable; otherwise, the model admits at least one positively periodic steady state. Numerical simulations elucidate that time heterogeneity enhances magnitudes of oscillations of animal population and brucella. Moreover, enlarging effective infection radii increases the risk of brucellosis propagations. As a result, we suggest that herdsmen should improve the sanitation of animals’ environment and isolate infected animals instantly to control brucellosis prevalence.

Analysis of the positive rate of anal swab nucleic acid test and clinical characteristics in patients with different severity of coronavirus disease 2019

To compared the positive rate of anal swab nucleic acid test and clinical characteristics of critical and general coronavirus disease 2019 (COVID-19) patients. Clinical data of 18 patients with COVID-19 admitted to the First People's Hospital of Lianyungang City from February to March 2020 were retrospectively analyzed. The patients were divided into general group (n = 11) and critical ill group (n = 7) according to the severity of the disease. The differences of gender, age, epidemiological characteristics, fever duration after admission, underlaying disease, positive rate of anal swab nucleic acid test at admission and two times of negative pharyngeal swab test were compared between the two groups. There were no significant differences in gender, age, fever duration after admission or underlaying disease between the two groups. The number of anorectal swab positive cases in critically ill group was significantly higher than that in general group (cases: 4 vs. 1, P = 0.047). After two negative pharyngeal swab nucleic acid test, the number of anal swab positive cases in critical illness group was still higher than that in general group (cases: 2 vs. 0), but the difference was not statistically significant (P = 0.137). The number of non-local infection in critical ill group was significantly higher than that in general group (cases: 4 vs. 0, P = 0.047). All of the 4 non-local infected patients had a history of living in Wuhan. The patients with anorectal swab nucleic acid positive may have a more serious condition. It may be a risk to transfer ill patients out of the isolation ward by the criteria of only two times of negative pharyngeal swab nucleic acid test. Patients returning to our city after infection in Wuhan may be more serious.

The differential impacts of non-locally acquired infections and treatment interventions on heterosexual HIV transmission in Hong Kong.

IntroductionHeterosexual infections have contributed to a high proportion of the HIV burden in Asia and Eastern Europe. Human mobility and non-local infections are important features in some cities/countries. An understanding of the determinants of the sustained growth of the heterosexual HIV epidemics would enable the potential impacts of treatment-based interventions to be assessed.MethodsWe developed a compartmental model for heterosexual HIV transmissions, parameterized by clinical and surveillance data (1984–2014) in Hong Kong. HIV sequence data were included for examining genetic linkages and clustering pattern. We performed sensitivity analyses to evaluate effects of high-risk sexual partnership and proportions of non-locally acquired infections. Four hypothetical interventions (a) immediate treatment, (b) enhancement of retention in care, (c) HIV testing campaigns, and (d) test-and-treat strategy, were examined.ResultsData of 2174 patients (723 female and 1451 male) diagnosed with HIV between 1984 and 2012 in Hong Kong were collected for model parameterization. Among 1229 sequences of non-MSM (men who have sex with men) patients, 70% were isolates and 17% were either dyads or triads. In base-case scenario, the total estimated number of new infections in 2012–2023 would be 672 for male and 452 for female. Following 100% retention in care intervention, the total proportion of averted new infections in 2012–2023 would be 7% for male and 10% for female. HIV testing campaign in 2012 and 2017 followed by 100% immediate treatment strategy would avert 5% and 9% of male and female new infections, respectively. In the epidemic model, an increase of high-risk sexual partnership from 6% to 9% would increase the epidemic growth (annual number of newly diagnosed and newly infected cases) by about 10%. If no non-locally acquired infection occurred as from 2012, the epidemic growth would slump. To control the heterosexual epidemic, periodic HIV testing at 5-year intervals with immediate treatment would avert 5–13% of annual new infections in 2013–2023.ConclusionsEnhanced HIV testing with immediate treatment is most effective in controlling the heterosexual epidemic, the impacts of which might however be attenuated by any increase of non-locally acquired infection, assuming little variations of high risk partnership over time.

Analysis of a reaction–diffusion SVIR model with a fixed latent period and non-local infections

This paper concerns with a reaction–diffusion susceptible-vaccinated-infectious-recovered model with a fixed latent period. The model is formulated as a non-local and time-delayed reaction–diffusion model due to the fact that an individual infected by the disease in one place may not stay at the same space in the domain due to the movement of human during the incubation period. We then derive the basic reproduction number as the spectral radius of the next infection operator and show that it serves as a threshold role in predicting whether the disease will spread. Further, the explicit formula of basic reproduction number is obtained when all model parameters to be positive constants and the domain to the one-dimensional case. Moreover, we demonstrate the differences in the form of basic reproduction number between the standard incidence and bilinear incidence rate.

Spatial dynamics of an epidemic model with nonlocal infection

Nonlocal infection plays an important role in epidemic spread, which can reflect the real rules of infectious disease. To understand its mechanism on disease transmission, we construct an epidemic model with nonlocal delay and logistic growth. The Turing space for the emergence of stationary pattern is determined by series of inequations by mathematical analysis. Moreover, we use the multi-scale analysis to derive the amplitude equation, and obtain rich pattern structures by controlling the variation of the delay parameter. As the increase of delay parameter, the degree of pattern isolation increase as well as the density of the infected population decrease which prohibits the propagation of the disease in space. The results systematically reveal the impact of nonlocal delay on the spread of infectious diseases and provide some new theoretical supports for controlling the spread of infectious diseases.

Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections

This paper is devoted to develop a nonlocal and time-delayed reaction-diffusion model for HIV infection within host cell-to-cell viral transmissions. In a bounded spatial domain, we study threshold dynamics in terms of basic reproduction numberR0for the heterogeneous model. Our results show that ifR0&lt;1, the infection-free steady state is globally attractive, implying infection becomes extinct, while ifR0&gt;1, virus will persist in the host environment.

Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections

We consider a class of non-cooperative reaction-diffusion system, which includes different types of incidence rates for virus dynamical models with nonlocal infections. Threshold dynamics are expressed by basic reproduction number \begin{document}$ R_0 $\end{document} in the following sense, if \begin{document}$ R_0 , the infection-free steady state is globally attractive, implying infection becomes extinct; while if \begin{document}$ R_0 > 1 $\end{document} , virus will persist. To study the invasion speed of virus, the existence of travelling wave solutions is studied by employing Schauder's fixed point theorem. The method of constructing super-solutions and sub-solutions is very technical. The mathematical difficulty is the problem constructing a bounded cone to apply the Schauder's fixed point theorem. As compared to previous mathematical studies for diffusive virus dynamical models, the novelty here is that we successfully establish the general existence result of travelling wave solutions for a class of virus dynamical models with complex nonlinear transmissions and nonlocal infections.

Dynamical behavior of a new oncolytic virotherapy model based on gene variation

Oncolytic virotherapy is an experimental treatment of cancer patients. This method is based on the administration of replication-competent viruses that selectively destroy tumor cells but remain healthy tissue unaffected. In order to obtain optimal dosage for complete tumor eradication, we derive and analyze a new oncolytic virotherapy model with a fixed time period $τ $ and non-local infection which is caused by the diffusion of the target cells in a continuous bounded domain, where $τ $ is assumed to be the duration that oncolytic viruses spend to destroy the target cells and to release new viruses since they enter into the target cells. This model is a delayed reaction diffusion system with nonlocal reaction term. By analyzing the global stability of tumor cell eradication equilibrium, we give different treatment strategies for cancer therapy according to the different genes mutations (oncogene and antioncogene).

Global Stability of a Nonlocal Epidemic Model with Delay

In this work, we investigate the nonlocal time-delayed andreaction-diffusion epidemic model studied by Guo et al. [Z. Guo, F. Wang and X. Zou, Threshold dynamics of an infective disease model with a fixed latentperiod and non-local infections, J. Math. Biol. 65 (2012) 1387--410]. In thecase that the coefficients are independent of the spatial variable, we obtainthe global stability of the disease-free equilibrium and the unique endemicequilibrium, which partially answers the open problem proposed by Guo et al.

On a reaction–diffusion system modeling the dengue transmission with nonlocal infections and crowding effects

In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction–diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R0 is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R0.

Threshold dynamics of an infective disease model with a fixed latent period and non-local infections

In this paper, we derive and analyze an infectious disease model containing a fixed latency and non-local infection caused by the mobility of the latent individuals in a continuous bounded domain. The model is given by a spatially non-local reaction-diffusion system carrying a discrete delay associated with the zero-flux condition on the boundary. By applying some existing abstract results in dynamical systems theory, we prove the existence of a global attractor for the model system. By appealing to the theory of monotone dynamical systems and uniform persistence, we show that the model has the global threshold dynamics which can be described either by the principal eigenvalue of a linear non-local scalar reaction diffusion equation or equivalently by the basic reproduction number R₀ for the model. Such threshold dynamics predicts whether the disease will die out or persist. We identify the next generation operator, the spectral radius of which defines basic reproduction number. When all model parameters are constants, we are able to find explicitly the principal eigenvalue and R₀. In addition to computing the spectral radius of the next generation operator, we also discuss an alternative way to compute R₀.

Epidemics with short and long-range interactions: role of vector dispersal patterns

We study the properties of the SIDRV (Susceptible-Infectious-Detected-Recovered-Vaccinated) model of the epidemic spread with local and non-local infection spread. The local spread is introduced by the nearest neighbors’ interactions while the non-local spread is produced by vectors performing a random walk onto the system topology. Within the model we focus on a study of vectors’ properties and on the interplay between vectors’ characteristics and their dispersal patterns. We search for a type of a random walk which maximizes the time for which vectors are in the infectious state and consequently contribute to the (non-local) infection spread for the longest time. We also search for a type of a random walk which leads to the highest severity of epidemics. On the basis of numerical simulations we can conclude that from the whole considered class of random walks some are favored over others. We also show a very different performance and sensitivity of efficiency measures related to time and epidemics severity. Finally, we assess the role of assumptions taken within the model and discuss its relevance in designing elimination strategies, showing crucial role of local control strategies.

Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an n-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latency and a non-local term caused by the mobility of the individuals during the latent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number R0 is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if R0<1, and becomes unstable if R0>1. In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When n = 2, two special cases allowing reducible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the disease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.