We study the effect of electric charge in compact stars assuming that the charge distribution is proportional to the mass density. The pressure and the density of the matter inside the stars are large, and the gravitational field is intense. This indicates that electric charge and a strong electric field can also be present. The relativistic hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff equation, is modified in order to include electric charge. We perform a detailed numerical study of the effect of electric charge using a polytropic equation of state. We conclude that in order to see any appreciable effect on the phenomenology of the compact stars, the electric fields have to be huge (∼ 10 21 V/m), which implies that the total charge is Q ∼ 10 20 Coulomb. From the local effect of the forces experienced on a single charged particle, it is expected that each individual charged particle is quickly ejected from the star. This in turn produces a huge force imbalance, and the gravitational force overwhelms the repulsive Coulomb and fluid pressure forces. The star can then collapse to form a charged black hole before all the charge leaves the system.

Following the 2013–14 outbreak in French Polynesia, the Zika virus (ZIKV) epidemic spread widely to many countries where Aedes Aegypti as the main transmitting vector is endemic. The lack of a second wave of ZIKV infection in most affected regions may suggest that a sufficiently high level of herd immunity was reached during the first wave. We developed an agent-based transmission model to investigate the role of asymptomatic infection on the likelihood of observing a second wave, while accounting for its relative transmissibility. We found that, as the relative transmissibility of asymptomatic infection increases, a second wave is more likely to occur, despite an increase in the attack rate during the first wave. When the reproduction number varies between 1.9 and 2.8 based on estimates for Antioquia, Colombia, the attack rate varies between 4% and 26% for a low (below 10%) effectiveness of interventions in blunting the ZIKV transmission from symptomatic cases to mosquitoes. Moreover, the fraction of cases due to sexual transmission is estimated below 4% of the cumulative incidence. Our analyses underscore the need to quantify the transmissibility of asymptomatic infections, without which the overall attack rates and the level of herd immunity cannot be accurately estimated.

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A new mathematical model incorporating epidemiological features of the co-dynamics of tuberculosis (TB) and SARS-CoV-2 is analyzed. Local asymptotic stability of the disease-free and endemic equilibria are shown for the sub-models when the respective reproduction numbers are below unity. Bifurcation analysis is carried out for the TB only sub-model, where it was shown that the sub-model undergoes forward bifurcation. The model is fitted to the cumulative confirmed daily SARS-CoV-2 cases for Indonesia from February 11, 2021 to August 26, 2021. The fitting was carried out using the fmincon optimization toolbox in MATLAB. Relevant parameters in the model are estimated from the fitting. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established through the application of Pontryagin’s Principle. Different control strategies: face-mask usage and SARS-CoV-2 vaccination, TB prevention as well as treatment controls for both diseases are considered. Simulations results show that: (1) the strategy against incident SARS-CoV-2 infection averts about 27,878,840 new TB cases; (2) also, TB prevention and treatment controls could avert 5,397,795 new SARS-CoV-2 cases. (3) In addition, either SARS-CoV-2 or TB only control strategy greatly mitigates a significant number of new co-infection cases.