Dengue fever is a vector-borne viral disease which is now endemic in more than 100 countries affecting more than 2.5 billion people worldwide. In recent years, dengue fever has become a major threat to public health in Pakistan. In this paper, we derived an explicit formula for reproduction number R0 (the most important epidemiological parameter) and then used real data of dengue fever cases of different hospitals of Lahore (Pakistan) on R0. Conditions for local stability of equilibrium points are discussed. In the end, simulations are carried out for different situations.
The low-temperature sintering of (Bi0.5Na0.5)TiO3-based ceramics can be achieved by sintering aid CuO. Piezoelectric ceramics (1 - x)[0.90(Bi0.5Na0.5)TiO3 - 0.10SrTiO3] - xCuO (BNT-ST-Cu) with x = 0, 0.01, 0.02, 0.03, and 0.04 were prepared through the mixed oxide route. A tetragonal structure was indexed for the undoped sample. Its structure was found to be changed to a pseudocubic when Cu was added. For undoped Cu samples, the sintering temperature (T s) for sufficient densification was 1160 °C. However, T s was reduced to 1090-1120 °C for Cu-added specimens. Field emission scanning electron microscopy (FE-SEM) showed a uniform and dense grain morphology for all samples. The maximum dielectric constant temperature (T m) was decreased with the doping concentration of Cu and applied frequency. The strain was increased with Cu concentration and had the maximum value of 500 pm/V for the sample x = 0.02 with symmetric and slim strain loops.