Phenomenological models are particularly useful for characterizing epidemic trajectories because they often offer a simple mathematical form defined through ordinary differential equations (ODEs) that in many cases can be solved explicitly. Such models avoid the description of biological mechanisms that may be difficult to identify, are based on a small number of model parameters that can be calibrated easily, and can be utilized for efficient and rapid forecasts with quantified uncertainty. These advantages motivate an in-depth examination of 37 data sets of epidemic outbreaks, with the aim to identify for each case the best suited model to describe epidemiological growth. Four parametric ODE-based models are chosen for study, namely the logistic and Gompertz model with their respective generalizations that in each case consists in elevating the cumulative incidence function to a power $p\in [0, 1]$. This parameter within the generalized models provides a criterion on the early growth behavior of the epidemic between constant incidence for $p = 0$, sub-exponential growth for $0 < p < 1$ and exponential growth for $p = 1$. Our systematic comparison of a number of epidemic outbreaks using phenomenological growth models indicates that the GLM model outperformed the other models in describing the great majority of the epidemic trajectories. In contrast, the errors of the GoM and GGoM models stay fairly close to each other and the contribution of the adjustment of $p$ remains subtle in some cases. More generally, we also discuss how this methodology could be extended to assess the "distance" between models irrespective of their complexity.

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We utilize the case incidence and mortality data to estimate the transmission potential and generate short-term forecasts of the COVID-19 pandemic to inform the public health policies using previously validated mathematical models. The analysis is augmented by the examination of geographic heterogeneity of COVID-19 at the departmental level along with the investigation of mobility and social media trends. Overall, the national and regional reproduction numbers show sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Whereas the most recent estimates of reproduction number indicate disease containment, with R_t<1.0 as of October 31, 2021. On the forecasting front, the sub-epidemic model performs best at capturing the 30-day ahead COVID-19 trajectory compared to the Richards and generalized logistic growth model. Nevertheless, the spatial variability in the incidence rate patterns across different departments can be grouped into four distinct clusters. As the case incidence surged in July 2020, an increase in mobility patterns was also observed. On the contrary, a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued, indicating the pandemic fatigue in the country.

This study presents a mathematical model of the transmission and spread of the Echinococcus granulosus parasite. The model incorporates host mobility, laws governing the dynamics of Echinococcosis transmission between hosts, and control and prevention measures. The basic reproductive number of the proposed model is calculated, and a sensitivity analysis is performed to identify the parameters that most influence the dynamics of transmission and spread of the disease among its hosts. The study evaluates two control strategies—dog deworming and sheep vaccination—based on their respective target reproductive numbers. The impact of these control and prevention measures is investigated through numerical simulations, which reveal that the dog deworming strategy consistently reduces infections in humans. In contrast, the sheep vaccination strategy demonstrates a more favorable scenario for disease eradication in both hosts. In addition, simulations show a close relationship between the early detection of the disease and the recovery of the patient.