The COVID-19 pandemic has caused widespread infections, deaths, and substantial economic losses. Vaccine development efforts have led to authorized candidates reducing hospitalizations and mortality, although variant emergence remains a concern. Peru faced a significant impact due to healthcare deficiencies. This study employed logistic regression to mathematically model COVID-19’s dynamics in Peru over three years and assessed the correlations between cases, deaths, and people vaccinated. We estimated the critical time (t_c) for cases (627 days), deaths (389 days), and people vaccinated (268 days), which led to the maximum speed values on those days. Negative correlations were identified between people vaccinated and cases (−0.40) and between people vaccinated and deaths (−0.75), suggesting reciprocal relationships between those pairs of variables. In addition, Granger causality tests determined that the vaccinated population dynamics can be used to forecast the behavior of deaths (p-value < 0.05), evidencing the impact of vaccinations against COVID-19. Also, the coefficient of determination (R²) indicated a robust representation of the real data. Using the Peruvian context as an example case, the logistic model’s projections of cases, deaths, and vaccinations provide crucial insights into the pandemic, guiding public health tactics and reaffirming the essential role of vaccinations and resource distribution for an effective fight against COVID-19.

The monkeypox virus (MPXV) has caused an unusual epidemiological scenario—an epidemic within a pandemic (COVID-19). Despite the inherent evolutionary and adaptive capacity of poxviruses, one of the potential triggers for the emergence of this epidemic was the change in the status of orthopoxvirus vaccination and eradication programs. This epidemic outbreak of HMPX spread worldwide, with a notable frequency in Europe, North America, and South America. Due to these particularities, the objective of the present study was to assess and compare cases of HMPX in these geographical regions through logistic and Gompertz mathematical modeling over one year since its inception. We estimated the highest contagion rates (people per day) of 690, 230, 278, and 206 for the world, Europe, North America, and South America, respectively, in the logistic model. The equivalent values for the Gompertz model were 696, 268, 308, and 202 for the highest contagion rates. The Kruskal–Wallis Test indicated different means among the geographical regions affected by HMPX regarding case velocity, and the Wilcoxon pairwise test indicated the absence of significant differences between the case velocity means between Europe and South America. The coefficient of determination (R²) values in the logistic model varied from 0.8720 to 0.9023, and in the Gompertz model, they ranged from 0.9881 to 0.9988, indicating a better fit to the actual data when using the Gompertz model. The estimated basic reproduction numbers (${\mathcal{R}}_0$) were more consistent in the logistic model, varying from 1.71 to 1.94 in the graphical method and from 1.75 to 1.95 in the analytical method. The comparative assessment of these mathematical modeling approaches permitted the establishment of the Gompertz model as the better-fitting model for the data and the logistic model for the ${\mathcal{R}}_0$. However, both models successfully represented the actual HMPX case data. The present study estimated relevant epidemiological data to understand better the geographic similarities and differences in the dynamics of HMPX.

Background: Monkeypox (Mpox) is a re-emerging zoonotic disease caused by the monkeypox virus (MPXV). Transmission occurs primarily through direct contact with lesions or contaminated materials, with sexual transmission playing a significant role in recent outbreaks. In 2022, Mpox triggered a major global outbreak and was declared a Public Health Emergency of International Concern (PHEIC) by the World Health Organization (WHO), prompting renewed interest in effective control strategies. Methods: This study developed a compartmental SEIR-based model to assess the epidemiological impact of key interventions, including vaccination and isolation, while incorporating critical epidemiological parameters. Sensitivity analyses were conducted to examine (1) disease dynamics in relation to the basic reproduction number, and (2) how different parameters influence the curve of symptomatic infections. Real-world continental-scale data were used to validate the model and identify the parameters that most significantly affect epidemic progression and potential control of Mpox. Results: Results showed that the basic reproduction number was most influenced by the recovery rate, vaccination rate, vaccine effectiveness, and transmission rates of symptomatic and asymptomatic individuals. In contrast, the progression of symptomatic cases was highly sensitive to the case fatality rate and incubation rate. Conclusions: These findings highlight the importance of integrated public health strategies combining vaccination, isolation, and early transmission control to mitigate future Mpox outbreaks.

The objective of the research is to estimate the transmission rate of an infection (β) in the SI epidemical model, using Bayesian statistical methods from observed data in Peru. After studying the SI mathematical model and Bayesian statistical inference metho'ds, a Bayesian estimator is proposed to estimate the transmisión rate of an infection in this model and a procedure is proposed to estimate this rate using Montecarlo simulation based on Markov chains - MCMC.

In this study, we develop and analyze an extended SEIR-type compartmental model that incorporates vaccination and treatment to describe the dynamics of acute respiratory infection transmission. The model subdivides the infectious population into several symptomatic stages and an asymptomatic class, which allows the evaluation of control strategies across different levels of infection severity. The basic reproduction number ${\mathcal{R}}_0$ is analytically derived, and its sensitivity to vaccination and treatment rates is examined to assess the impact of public health interventions on epidemic control. Numerical simulations demonstrate that the joint implementation of vaccination and treatment can markedly reduce disease prevalence and lead to infection elimination when ${\mathcal{R}}_0<1$. The results emphasize the critical role of parameter interactions in determining disease persistence and show that combining both interventions produces stronger epidemiological effects than either one alone. Machine learning techniques, specifically Support Vector Machines (SVMs), are employed to classify epidemiological outcomes and support parameter estimation. The biological markers evaluated were not effective discriminants of infection status, underscoring the importance of integrating mechanistic modeling with data-driven approaches. This combined framework enhances the understanding of epidemic dynamics and improves the predictive capacity for decision-making in public health.

Se propone una modificación del modelo epidemiológico SLIAR (Susceptible-Latente- Infectado Sintomático-Asintomático-Recuperado) con dinámica vital. Este modelo incluye una estrategia de control por vacunación, y un tratamiento para reducir los síntomas, además la población infectada sintomática se divide en dos estados según su gravedad. El análisis cualitativo muestra la estabilidad local del punto de equilibrio libre de enfermedad y el punto endémico. Las simulaciones y el análisis estadístico de sensibilidad son desarrollados utilizando un conjunto de parámetros para COVID-19, finalmente, encontramos que las tasas de transmisión, reclutamiento y vacunación son objetivos potenciales para controlar un brote epidémico.