Standard routine techniques of modeling of tick-borne encephalitis

Abstract

Tick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R 0-like threshold has been derived by using the next-generation matrix method. The formula for R 0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.

Keywords

• mathematical modeling
• stability
• vector-borne disease
• encephalitis
• basic reproduction number
• immune