Dynamic behavior of a parasite–host model with general incidence

AbstractIn this paper, we consider the global dynamics of a microparasite model with more general incidences. For the model with the bilinear incidence, Ebert et al. [D. Ebert, M. Lipsitch, K.L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist 156 (2000) 459–477] observed that parasites can reduce host density, but the extinction of both host population and parasite population occurs only under stochastic perturbations. Hwang and Kuang [T.W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol. 46 (2003) 17–30] studied the model with the standard incidence and found that the host population may be extinct in the absence of random disturbance. We consider more general incidences that characterize transitions from the bilinear incidence to the standard incidence to simulate behavior changes of populations from random mobility in a fixed area to the mobility with a fixed population density. Using the techniques of Xiao and Ruan [D. Xiao, S. Ruan, Global dynamics of a ratio-dependent predator–prey system, J. Math. Biol. 43 (2001) 268–290], it is shown that parasites can drive the host to extinction only by the standard incidence. The complete classifications of dynamical behaviors of the model are obtained by a qualitative analysis

MODELING THE DYNAMICS OF INFECTIOUS DISEASES WITH Latency IN SPATIALLY HETEROGENEOUS Environments

Assuming that an infectious disease has a fixed latent period and latent individuals in the population may disperse in a spatially heterogeneous environment, we derive three new models of SIR type, which are more realistic than the existing related ones. The first one considers a 2-patch environment and ignores the demographic structure. The model is given by a system of delay differential equations (DDEs). It is a generalization of the classical Kermack-McKendrick SIR model, and it preserves some properties that the Kermack-McKendrick model processes. We show that the ratio of final sizes in two patches is fully determined by the ratio of dispersion rates of susceptible individuals between the two patches. We also numerically explore the patterns by which the disease dies out and have observed multiple outbreaks of the disease before it goes to extinction. The second model considers a general n-patch environment but incorporates a simple demographic structure, also resulting in a system of DDEs. Assuming the irreducibility of dispersal rates matrices of the infected classes, an expression of the basic reproduction number Ro is obtained. It is shown that disease free equilibrium is globally asymptotically stable if Ro \u3c 1, and unstable if Ro \u3e 1. In the latter case, there is at least one interior equilibrium and the disease is uniformly persistent. For n = 2, two special cases are considered to obtain more detailed results on how the disease latency and the population dispersal jointly affect the disease dynamics. The third model deals with a spatially continuous environment, and is given by a delayed system of reaction-diffusion equations with a spatially non-local term. We address the well-posedness of the model but the main concern is traveling wave fronts iii of the model. We obtain a critical value c* which is shown to be a lower bound for the wave speed of traveling wave fronts. Although we can not prove that this value is exactly the minimal wave speed, numeric simulations seem to suggest that it is. Furthermore, the simulations on the model equations also suggest that the disease spread speed coincides with c*. We also discuss how the model parameters affect c*

Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period

A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease

Transmission Dynamics of a Two-City SIR Epidemic Model with Transport-Related Infections

A two-city SIR epidemic model with transport-related infections is proposed. Some good analytical results are given for this model. If the basic reproduction number ℜ0γ≤1, there exists a disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number ℜ0γ>1. We also show the permanence of this SIR model. In addition, sufficient conditions are established for global asymptotic stability of the endemic equilibrium

Uniform and strict persistence in monotone skew-product semiflows with applications to non-autonomous Nicholson systems

Producción CientíficaWe determine sufficient conditions for uniform and strict persistence in the case of skew-product semiflows generated by solutions of non-autonomous families of cooperative systems of ODEs or delay FDEs in terms of the principal spectrums of some associated linear skew-product semiflows which admit a continuous separation. Our conditions are also necessary in the linear case. We apply our results to a noncooperative almost periodic Nicholson system with a patch structure, whose persistence turns out to be equivalent to the persistence of the linearized system along the null solution.MINECO/FEDER MTM2015-6633

Stability criteria for a multi-city epidemic model with travel delays and infection during travel

We present a compartmental SIR (susceptible-infected-recovered) model to describe the propagation of an infectious disease in a human population, when individuals travel between pp different cities. The time needed for travel between any two locations is incorporated, and we assume that disease progression is possible during travel. The model is equivalent to an autonomous system of differential equations with multiple delays, and each delayed term is defined through a system of ordinary differential equations. We establish some necessary and sufficient conditions for the disease-free equilibrium of the model to be asymptotically stable

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

Background Despite the vaccination process in Germany, a large share of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests. Methods We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type, metapopulation model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the regions (German counties) are initialized randomly with incidences between 75 and 150 weekly new cases per 100,000 inhabitants (red zones) or below (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20% of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario. Results We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, the negative effect of less strict interventions can be overcome by high commuter testing rates. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable. If less strict interventions are in favor, substantially increased testing rates are needed to avoid overall higher infection dynamics. Conclusions Our results indicate that local containment of outbreaks and maintenance of low overall incidence is possible even in densely populated and highly connected regions such as Germany or Western Europe. While we demonstrate this on data from Germany, similar patterns of mobility likely exist in many countries and our results are, hence, generalizable to a certain extent

FLUed: A Novel Four-Layer Model for Simulating Epidemic Dynamics and Assessing Intervention Policies

From the 2003 severe acute respiratory syndrome (SARS) epidemic, to the 2009 swine-origin influenza A (H1N1) pandemic, to the projected highly pathogenic avian influenza A event, emerging infectious diseases highlight the importance of computational epidemiology to assess potential intervention policies. Hence, an important and timely research goal is a general-purpose and extendable simulation model that integrates two major epidemiological factors—age group and population movement—and substantial amounts of demographic, geographic, and epidemiologic data. In this paper, we describe a model that we have named FLUed for Four-layer Universal Epidemic Dynamics that integrates complex daily commuting network data into multiple age-structured compartmental models. FLUed has four contact structures for simulating the epidemic dynamics of emerging infectious diseases, assessing the potential efficacies of various intervention policies, and identifying the potential impacts of spatial-temporal epidemic trends on specific populations. We used data from the seasonal influenza A and 2009 swine-origin influenza A (H1N1) epidemics to validate model reliability and suitability and to assess the potential impacts of intervention policies and variation in initial outbreak areas for novel/seasonal influenza A in Taiwan. We believe that the FLUed model represents an effective tool for public health agencies responsible for initiating early responses to potential pandemics