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.