Infectious disease outbreaks are recurring events which can lead to a large number of fatalities every year. Infectious disease outbreaks occur infrequently and the role of global warming and modes of climate variability for those outbreaks is not clear. Here we use an extreme value statistics approach to examine annual spatially aggregated infectious disease fatality data to compute their probability to occur using generalized Pareto distribution (GPD) models. The GPD provides a good model for modeling the fatality data and reveals that the number of fatalities follows a power-law. We find that the magnitude of Covid-19 is of an expected level given previous fatality data over the period 1900-2020. We also examined whether including co-variates in the GPD models provide better model fits. We find evidence that a pure linear trend is the best co-variate and, thus, has increased the propensity of large outbreaks to occur for most continents and world-wide. This suggests that mainly non-climate factors affect the likelihood of outbreaks. This linear trend function provides a crude representation of socio-economic trends such as improved public health. However, for South America the Atlantic multidecadal oscillation modulates the outbreak propensity as the best co-variate, showing that climate can play some role in infectious disease outbreaks in some regions.