A cellular automata model is developed aiming to study the epidemic on a lattice of two dimensions. The characteristics of individual including reproduction, death by inherited diseases and age are studied in the Penna model. The spreading of epidemic and the reproduction of individual are considered as cellular automata. We shall mainly discuss the influence on the number of epidemical patients by infection rate and death rate. The results show that the existence of epidemic mainly depends on the infection rate and the death rate but not the initial ratio of patients. There are two reasons for nonexistent epidemic. As long as the infection rate is less than 0.3, the epidemic cannot spread. On the other hand, if the infection rate and the death rate are both high, the individuals with epidemic die out and the epidemic cannot spread, either. The epidemic can exist all along when the combination of infection rate and death rate are in the mid area.
The phenomenon of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The SIR model with incubation time is used. In our model the localization of individuals in different social groups, the effectiveness of different interpersonal interactions and the mobility of a contemporary community are taken into account. The influence of different control methods on the spreading process is investigated as a function of different initial conditions. The cost-effectiveness of mass preventive random vaccinations, target vaccinations and sick leaves are compared. A critical range of vaccinations, sufficient for suppressing of an epidemic is calculated. The results of numerical calculations are similar to the solutions of the master equation for the spreading process.
We study the effect of networks interconnection on the epidemic cost of them. When an epidemic will eventually die out, we find that the total cost of the epidemic over the interconnected network is approximate to the sum of the total epidemic cost of the two sub-networks. We also prove that the interconnection behavior can reduce epidemic threshold. Thus network interconnecting makes an epidemic more easily to occur, while keeping the total cost of the epidemic almost unchanged.
The results of Kermack–McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of an epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like susceptible-infected-removed (SIR) model. The motion of the circular front of an infected cluster shows a linear behavior in time. The correlation of a particular site to be infected with respect to the central site is also studied. The outcomes of the CA model are in good agreement with those obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed a considerable amount of light on the physical properties of the spread of a typical epidemic in a simple, yet robust way.
In this paper, we consider the spread of an epidemic on a changing network, specifically focusing on two phenomena. The first part of the paper investigates a possible mechanism of disease outbreaks on college campuses. We present a toy model, dividing students into extroverts (high-degree nodes with a large number of contacts) and introverts (low-degree nodes with a small number of contacts). In our model, the average degree of extroverts is evolving with time, and its dynamics is coupled with the current epidemic situation: extroverts tend to increase their number of contacts for low level of epidemic, but as more and more students get infected, they start decreasing their average degree. Another phenomenon analyzed in the paper is vaccination: how should the vaccine be allocated to best benefit the population? We consider two possible vaccination strategies: (1) vaccinating people starting from high risk groups (older people with a higher risk of mortality) or (2) prioritizing vaccination of people with a higher number of contacts (such as college students) to decrease the epidemic outbreak. Both phenomena show the importance of diversity in the number of contacts.
Optimal allocation of vaccine doses is a major challenge faced by the health authorities especially in the case of an ever-growing pandemic expansion and a limited supply availability. Based on a spatio-temporal compartmental virus propagation model applied to the case of SARS-CoV-2 virus, we investigate a layered vaccine allocation strategy for the subpopulations of a given country or a geographical region based on the prevalence of susceptible individuals as a prioritization metric. Our findings show that a relaxed layered allocation prioritization, where a maximum of regions benefit from vaccine doses is more effective in controlling the epidemic than a strict prioritization, focused only on the few most prioritized regions. These results are consistent among different vaccine rollout speeds for various limiting values of the priority list.
Most literature works on estimating treatment effects assume that the observed data are either under the specific “treatment” or not. However, in many cases, the observed data could be subject to multiple treatments. We propose to combine econometric methods developed for different purposes to disentangle the multiple treatment effects. We illustrate this strategy by considering the impact of global pandemic v.s. the strictest “lockdown” policy of Hubei, China implemented in January, 2020. We show that although the strictest “lockdown” policy quickly contained the spread of COVID-19, it also inflicted huge economic loss on Hubei economy. It lowered Hubei GDP by about 37% compared to the level had there been no “lockdown” under the pandemic. However, even though Hubei economy managed to recover from the “lockdown”, it could not escape the global impact of pandemic. Its economy is still about 90% of the level had there been no pandemic.
Based on the stress responses of individuals, the susceptible-infected-susceptible epidemic model was improved on the small-world networks and BA scale-free networks and the simulations were implemented and analyzed. Results indicate that the behaviors of individual’s stress responses could induce the epidemic spreading resistance and adaptation at the network level. This phenomenon showed that networks were learning how to adapt to the disease and the evolution process could improve their immunization to future infectious diseases and would effectively prevent the spreading of infectious diseases.
In this paper, a new spreading network was constructed and the corresponding immunizations were proposed. The social ability of individuals in the real human social networks was reflected by the node strength. The negativity and positivity degrees were also introduced. And the edge weights were calculated by the negativity and positivity degrees, respectively. Based on these concepts, a new asymmetric edge weights scale-free network which was more close to the real world was established. The comparing experiments indicate that the proposed immunization is priority to the acquaintance immunization, and close to the target immunization.
In this paper, a two-layer network on various immunization strategies in the post-epidemic era is constructed and an improved symbiotic evolutionary model of COVID-19 and information collaboration is proposed. The dynamic transformation probability is introduced to influence the virus information transmission coevolutionary process. The dynamic transformation probability is influenced by the immunization strategies and vertex characteristics. We quantify the effects of immunization strategy, node properties, global temperature, and collaborative information dissemination on new crown outbreaks. We simulated our model in a scale-free network to analyze the propagation. The evolutionary phenomenon of the network during propagation was investigated. We simulated the proven epidemic information coevolutionary model in a two-layer network, validated it with real data comparisons by proving that our proposed model fits the real situation.
The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small basic reproduction number and transmission coefficient of asymptomatically-infected individuals. If asymptomatic individuals transmit at a rate that is at least 20% that of symptomatic individuals, quarantine is always more effective. The study further shows that the reduction in disease burden obtained from a combined quarantine and isolation program can be comparable to that obtained by a vaccination program, if the former is implemented quickly enough after the onset of the outbreak. If the implementation of such a quarantine/isolation program is delayed, however, even for a short while, its effectiveness decreases rapidly.
During the initial phase of an epidemic, individual displacements between different regions modify the contact patterns. Understanding mobility processes and their consequences is necessary to predict the subsequent spread of the disease in order to optimize control policies. The basic reproduction number is commonly used to determine the threshold between extinction and expansion of the disease. Once it is derived for an epidemic model that includes the travel of population between distinct localities, the dependence of the diseases dynamics upon travel rates becomes explicit. In this study, we examine the effects of travel on the epidemic threshold for a model of two communities. The travel rates are treated as varying subject to two scenarios. We show theoretically that if the transmission potentials within communities are moderate, the epidemic threshold can be modified by travel. The conditions for the presence of the threshold induced by travel is determined and the critical values of travel at which the basic reproduction number is equal to one are derived. We show further that these results can also be applied to a model of three communities under specific travel patterns and that the derived basic reproduction number has a form similar to that of the two communities problem.
Demographics have significant effects on disease spread in populations and the topological evolution of the underlying networks that represent the populations. In the context of network-based epidemic modeling, Markov chain-based approach and pairwise approximation are two powerful tools — the former can capture stochastic effects of disease transmission dynamics and the latter can characterize the dynamical correlations in each pair of connected individuals. However, to our best knowledge, the study on epidemic spreading in networks relying on these two techniques is still lacking. To fill this gap, in this paper, a deterministic pairwise susceptible–infected–susceptible (SIS) epidemic model with demographics on complex networks with arbitrary degree distributions is studied based on a continuous time conditional Markov chain. This deterministic model is rigorously derived — using the moment generating function — from the Kolmogorov differential equations for the evolution of individuals and pairs. It is found that demographics will induce the extinction of the disease by reducing the basic reproduction number or lowering the epidemic prevalence after the disease prevails. Moreover, due to the demographical effects, the resulting network tends to a homogeneous network with a degree distribution similar to Poisson distribution, irrespective of the initial network structure. Additionally, we find excellent agreement between numerical solutions and individual-based stochastic simulations using both Erdös–Renyi (ER) random and Barabási–Albert (BA) scale-free initial networks. Our results may provide new insights on the understanding of the influence of demographics on epidemic dynamics and network evolution.
It is argued that the (quasi-) mechanistic modelling of the incidence of an infectious disease in a population of varying size is a nontrivial problem, deserving careful thinking. The spread of a virus among seals is used to illustrate how a submodel for the contact process may be helpful. In that same context the impact of the disease on the population growth of the host is investigated.
We analysed a model for the interaction of a macroparasite and a host population growing logistically. The model is obtained by approximating the parasite distribution with a negative binomial with a fixed clumping parameter.
By letting the contact rate k vary, we found a complex pattern of bifurcations, including subcritical bifurcations of the disease-free equilibrium, Hopf and homoclinic bifurcations. The specific pattern depends on the interaction of the various parameters; in particular, alternative stable equilibria may occur only when the carrying capacity KN is sufficiently large, while periodic solutions may occur for all values of KN, if k is large enough.
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Viral liver infections with parenteral transmission in Western countries are mostly caused by hepatitis B and hepatitis C viruses (HBV and HCV). This paper presents a mathematical model that describes the history of the spread of HBV and HCV infections in the general population in Italy. The analysis of the model and the results also provide some new insight into the mechanisms of the epidemics. The model structure is based on an underlying analysis of the various effects of the infection progression in the host, in order to incorporate into its parameters most of the information available from the literature. Moreover, incidence and prevalence curves of both HBV and HCV infections and of HBV/HCV co-infections are generated and qualitative aspects of the epidemic, such as possible endemic steady states and the basic reproduction number, are also analyzed.
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