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Ilham Saiful Fauzi 《Journal of Nonlinear Modeling and Analysis》2024,6(3):693-711

Dengue fever is a vector-borne viral disease that has become a worrisome health issue in tropical and subtropical countries. The seasonal trend of dengue incidence encourages outbreaks with a high risk of infection at particular periods annually that potentially resulted in a significant economic burden. The epidemiological mathematical model, the SIR-SI model, is modified by considering the time-dependent and periodic-forced infection rate parameter through sinusoidal functions to obtain well data fitting. We show the existence and the stability of the disease-free and endemic equilibria for the system and their relation to the basic reproduction number of the disease. Next, we adapt the insurance concept to develop an insurance mathematical model that accommodates the proposed dengue transmission model in calculating nominal premiums. An increase in the basic reproduction number as an important indicator of the level of disease transmission risk resulted in an increase in the nominal premium. We also introduce a reserve function that guarantees sufficient premium payments collected by insurer to cover up future expenditure due to dengue outbreaks. Through this reserve function, we obtain an adjusted premium as a minimum value of premium which ensures that the reserve function is always positive. Mathematical models combined with insurance features have the potential to become important tools for relevant authorities to gain insight into disease transmission dynamics as well as assess the economic burden induced by the occurrence of disease outbreaks.  相似文献   

    

《Journal of Colloid Science》1952,7(5):453-464

Micelle formation by the oil-dispersible soap, calcium xenylstearate, in moist benzene has been studied by fluorescent dye techniques, utilizing Rhodamine B and Acridine Orange. A treatment is presented for the interpretation of fluorescence depolarization data obtained from a system in which the emitting dye is present partly as a component of soap micelles and partly in true molecular solution. This method has special usefulness for identifying the onset of micelle formation in very dilute solutions. The midpoint of the critical range for the formation of micelles in this case is found to be 0.6 × 10⁻⁶ mole/l.; the size of the micelles is essentially constant over the range from 1 × 10⁻⁶ to 7 × 10⁻³ mole/l. The data obtained are consistent with a simple mass law equilibrium between molecularly dissolved and micellar soap. A knowledge of this equilibrium provides guidance in the development of improved rust-inhibiting oils.  相似文献