1COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human 2 health. The development of quantitative approaches to advance comprehension of the current outbreak 3 is urgently needed to tackle this severe disease. In this work, several mathematical models are proposed 4 to represent SARS-CoV-2 dynamics in infected patients. Considering different starting times of 5 infection, parameters sets that represent infectivity of SARS-CoV-2 are computed and compared with 6 other viral infections that can also cause pandemics. 7Based on the target cell model, SARS-CoV-2 infecting time between susceptible cells (mean of 30 8 days approximately) is much slower than those reported for Ebola (about 3 times slower) and influenza 9 (60 times slower). The within-host reproductive number for SARS-CoV-2 is consistent to the values of 10 influenza infection (1.7-5.35). The best model to fit the data was including immune responses, which 11 suggest a slow cell response peaking between 5 to 10 days post onset of symptoms. The model with 12 eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. 13Interestingly, both, the target cell model and the model with immune responses, predict that virus may 14 replicate very slowly in the first days after infection, and it could be below detection levels during the 15 first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation 16 of standard parameters of viral infections is the key contribution of this pioneering work.

We present a model that incorporates two co-circulating viral diseases, Dengue and Chikungunya, where we allow secondary infections from either of the two diseases. We only consider one vector population, Ae. aegypti since in the Mexican region where we set our scenarios, only this species has been reported to transmit both viruses. We estimate the basic reproduction number and perform numerical simulations for dierent scenarios where we may observe coexistence of Dengue and Chikungunya; we also compare the results of the model with Dengue and Chikungunya data from Mexico 2015 and we obtain a good model t. To complete our ndings we perform a sensitivity analysis, and calculate the partial rank correlation coecients (PRCCs) to determine the parameter values inuence on the reproduction numbers and predict fate of the diseases.We show that R0 for each one of the viruses is highly sensitive to the mosquito biting rate and the transmission rates for both diseases with positive inuence and the average lifespan of mosquito along with the human recovery rate with negative inuence on both diseases. Our results are consistent with those of previous authors.

Key high transmission dates for the year 2020 are used to create scenarios to model the evolution of the COVID-19 pandemic in several states of Mexico for 2021. These scenarios are obtained through the estimation of a time-dependent contact rate, where the main assumption is that the dynamic of the disease is heavily determined by the mobility and social activity of the population during holidays and other important calendar dates. First, changes in the effective contact rate on predetermined dates of 2020 are estimated. Then, using the instantaneous reproduction number to characterize the status of the epidemic (Rt ≈ 1, Rt > 1 or Rt < 1), this information is used to propose different scenarios for the number of cases and deaths for 2021. The main assumption is that the effective contact rate during 2021 will maintain a similar trend to that observed during 2020 on key calendar dates. All other conditions are assumed to remain constant in the time scale of the projections. The objective is to generate a range of scenarios that could be useful to evaluate the possible evolution of the epidemic and its likely impact on incidence and mortality.

We will inevitably face new epidemic outbreaks where the mechanisms of transmission are still uncertain, making it difficult to obtain quantitative predictions. Thus we present a novel algorithm that qualitatively predicts the start, relative magnitude and decline of uncertain epidemic outbreaks, requiring to know only a few of its "macroscopic" parameters. The algorithm is based on estimating exactly the time-varying contact rate of a canonical but time-varying Susceptible-Infected-Recovered epidemic model parametrized to the particular outbreak. The algorithm can also be extended to other canonical epidemic models. Even if dynamics of the outbreak deviates significantly from the underlying epidemic model, we show the predictions of the algorithm remain robust. We validated our algorithm using real time-series data of measles, dengue and the current zika outbreak, comparing its performance to existing algorithms that also use a few macroscopic parameters (e.g., those estimating reproductive numbers) and to those using a thorough understanding of the mechanisms of the epidemic outbreak. We show our algorithm can outperform existing algorithms using a few macroscopic parameters, providing an informative qualitative evaluation of the outbreak.