Network epidemic models with two levels of mixing

The study of epidemics on social networks has attracted considerable attention recently. In this paper, we consider a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic on a finite network, having an arbitrary but specified degree distribution, in which individuals also make casual contacts, i.e. with people chosen uniformly from the population. The behaviour of the model as the network size tends to infinity is investigated. In particular, the basic reproduction number R(0), that governs whether or not an epidemic with few initial infectives can become established is determined, as are the probability that an epidemic becomes established and the proportion of the population who are ultimately infected by such an epidemic. For the case when the infectious period is constant and all individuals in the network have the same degree, the asymptotic variance and a central limit theorem for the size of an epidemic that becomes established are obtained. Letting the rate at which individuals make casual contacts decrease to zero yields, heuristically, corresponding results for the model without casual contacts, i.e. for the standard SIR network epidemic model. A deterministic model that approximates the spread of an epidemic that becomes established in a large population is also derived. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations work well, even for only moderately sized networks, and that the degree distribution and the inclusion of casual contacts can each have a major impact on the outcome of an epidemic.     

Mathematical Models for Hantavirus Infection in Rodents

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.     

A Fuzzy Reed–Frost Model for Epidemic Spreading

In this paper, we present a fuzzy approach to the Reed–Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated into the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem with data of the viral epidemic in a children daycare are performed and the results are compared with a stochastic Reed–Frost generalization.     

Effect of Predators of Juvenile Rodents on the Spread of the Hantavirus Epidemic

Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.     

Ebola in great apes – current knowledge,possibilities for vaccination,and implications for conservation and human health

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Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.