The effect of population dispersal on the spread of a disease

The effect of population dispersal among n patches on the spread of a disease is investigated. Population dispersal does not destroy the uniqueness of a disease free equilibrium and its attractivity when the basic reproduction number of a disease R₀<1. When R₀>1, the uniqueness and global attractivity of the endemic equilibrium can be obtained if dispersal rates of susceptible individuals and infective individuals are the same or very close in each patch. However, numerical calculations show that population dispersal may result in multiple endemic equilibria and even multi-stable equilibria among patches, and also may result in the extinction of a disease, even though it cannot be eradicated in each isolated patch, provided the basic reproduction numbers of isolated patches are not very large.     

Modeling the spread of Rubella disease using the concept of with local derivative with fractional parameter

Our aim in this work was to examine the model underpinning the spread of the Rubella virus using the novel derivative called beta‐derivative. The study of the equilibrium points together with the analysis of the disease free equilibrium points was presented. Due to the complexity of the modified equation, we introduced a new operator based on the Sumudu transform. The properties of this operator were proposed and proved in detail. We made used of this operator together with the idea of perturbation method to derive a special solution of the extended model. The stability of the method for solving this model was presented. The uniqueness of the special solution was presented, and numerical simulations were done. The graphical representations show that the model depends on both parameters and the fractional order. © 2015 Wiley Periodicals, Inc. Complexity 21: 442–451, 2016     

Crosslinking of an unsaturated polyester resin in the mould: Modelling and heat transfer studies

The crosslinking of unsaturated polyester was studied by using an experiment and a mathematical model of the process. Temperature–time profiles were recorded in the centre of the sample inside the mould at the outer wall of the cylindrical copper mould, and in the bulk of the heated air bath. A numerical model was constructed by taking into account the heat transferred by convection from the air to the mould surface and the heat transferred by conduction through the resin, as well as the heat generated by the crosslinking reaction. The convection heat transfer coefficient was determined in independent experiments with the empty copper mould. Introduction of the carbon base filler reduced the amount of heat generated in the composite due to the less reactive component in the composite. As a result, it lowered the temperature of the resin. By recording the temperature-time and the degree of crosslinking time profiles developed within the sample extensive knowledge of the process can be obtained. The effects of the convection heat transfer on the rate of mould heating, and the conduction heat transfer through the mould as well as the internal heat generated by the crosslinking reaction are visibly shown, despite a complexity of the process.     

Sustainable management of an alpine national park: handling the two-edged effect of tourism

Attracting visitors to an alpine national park can open up additional sources of funding for species conservation. However, tourism also brings ecologically negative impacts to the park and, in particular, to endangered species. In this paper, we discuss the handling of this two-edged effect of nature-based tourism within the context of a national park’s management decision. We develop a stylized model which frames the interaction of a representative largely unknown species, its habitat, and park visitors in an alpine ecosystem. In applying this to the protection of a rock partridge population in the Hohe Tauern National Park (Austria), we illustrate that a combined visitor and species protection policy can maximize steady state net benefits from tourism and conservation, while ensuring that the endangered species reaches its conservation target in the long run. Thus, even for a small, largely unknown species such as the rock partridge, and not only for popular species like the golden eagle, it is possible to endogenously generate a conservation budget by attracting visitors.     

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

TV and radio advertisements are widely acknowledged as important interventions in raising issues of public health care and play promising role to control the infection through propagating awareness among the individuals. In this paper, a nonlinear susceptible‐infected‐susceptible (SIS) model is proposed and analyzed to see the impacts of TV and radio advertisements on the spread of influenza epidemic. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals. The information regarding the protection against the disease is propagated via TV and radio advertisements, and their growth rates are assumed to be proportional to the fraction of infected individuals. However, the growth rate of TV advertisements decreases with the increase in number of aware individuals. The information broadcasted through TV and radio advertisements induces behavioral changes among the susceptible individuals, and they form an isolated aware class. The epidemiological feasible equilibria, their stability properties, and direction of bifurcation are discussed. The expression for modified basic reproduction number is obtained. The model analysis shows that the dissemination rate of awareness among susceptible individuals due to TV and radio advertisements and baseline number of TV and radio advertisements have potential to reduce the epidemic peak and, thus, control the spread of infection. Further, the analytical findings are well supported through numerical simulation.     

Detection of heterogeneity and estimation of population characteristics from the field survey data: 1987/88 Japanese feasibility study of the southern hemisphere Minke whales

To get reliable information of the age structure of whale population, Japan conducted a feasibility study of scientific research in the Antarctic in 1987/88. Though the sample was not large enough, it was the first data free from the problem of selectivity and whaling ground bias. From the analysis, it was found that the biological characteristics are highly heterogeneous spatially or other ways. Considering this, we recognize that the survey should be designed to collect the sample from the whole research area uniformly to obtain unbiased estimates of population characteristics. However, in an actual biological field survey, it is difficult to keep the sampling fractions thecisely the same for each sampling units. Therefore, it is important to detect the heterogeneity in the sample, and poststratify the data corresponding to the heterogeneity. The methodology of the estimation and model evaluation presented here will be useful for the development of biological field survey in general.