This number gives information whether the epidemic can be controlled. Notice, all epidemic models are characterized by the basic reproduction number R0.
The function of response in the predator-prey model is given by a Lotka-Volterra type. The epidemic disease is described by SEIR (Susceptible-Exposed-Infected-Recovered) and SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) models with a logistic growth function only in the susceptible prey population. In this paper, the author studies a predator-prey model based on epidemic disease.
Lastly, numerical simulations are illustrated to support the theoretical results and a comparison between the integer and fractional-order systems is presented. Next, with the aim of the stability theory of fractional-order systems, some conditions, which can guarantee the local stability of the fractional-order model, are developed and occurrence of forward and Hopf bifurcations in this model are studied. Using the methods of bifurcations theory, it is proved that the integer-order model exhibits forward bifurcation and Hopf bifurcation. The basic reproduction number \(_0<1\) in integer-order model. Firstly, the positivity and boundedness of solutions for integer-order model are proved. This means you get the best service directly from your pump manufacturer.This paper deals with the qualitative behavior of an integer and fractional-order SIR epidemic model with logistic growth of the susceptible individuals. KSB also provide you with spare parts quickly. KSB Service takes care of the commissioning, inspection, servicing and maintenance of your pumps, valves and complete systems directly on site. The experienced specialists are certified to ensure excellent quality and extensive experience. The KSB success formula for high-performance pumps lies in the technological strength in hydraulics, materials and automation.Ĭompetent service right from the start The numerous production facilities ensure that KSB as a pump manufacturer can guarantee customer proximity and first-class service. KSB ensures the operational reliability of its industrial pumps and valves. Achieving more than 1.5 million sales worldwide, Etanorm is the most successful standard water pump. Products convince with the most innovative technology as well as with systems that have been tried and tested for many years - including the Etanorm water pump. KSB pump manufacturers: the best solution for your plant Industrial pumps and valves from KSB cover a wide range of applications and are highly energy-efficient. Benefit from many years of experience and technical expertise as a renowned pump manufacturer. Thanks to innovative research and development, KSB can meet the most diverse requirements of customers. With more than 15,000 employees worldwide and its own sales and marketing, manufacturing facilities and service operations, KSB develops and produces custom-fit pumps for various applications.Īs an experienced pump manufacturer, its product portfolio includes building and industrial technology, water transport, wastewater treatment and power plant processes. KSB - one of the world's leading manufacturers of industrial valves and pumpsįounded in 1871 in Frankenthal (Germany), KSB has been one of the leading suppliers of pumps and industrial valves for over 150 years.
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