Human movement is a key factor in infectious diseases spread such as dengue. Here, we explore a mathematical modeling approach based on a system of ordinary differential equations to study the effect of human movement on characteristics of dengue dynamics such as the existence of endemic equilibria, and the start, duration, and amplitude of the outbreak. The model considers that every day is divided into two periods: high-activity and low-activity. Periodic human movement between patches occurs in discrete times. Based on numerical simulations, we show unexpected scenarios such as the disease extinction in regions where the local basic reproductive number is greater than 1. In the same way, we obtain scenarios where outbreaks appear despite the fact that the local basic reproductive numbers in these regions are less than 1 and the outbreak size depends on the length of high-activity and low-activity periods.

The human movement plays an important rol in the spread of infectious diseases. On an urban scale, people move daily to workplaces, schools, among others. Here, we are interested in exploring the effect of the daily local stay on the variations of some characteristics of dengue dynamics such as the transmission rates and local basic reproductive numbers. For this, we use a two-patch mathematical model that explicitly considers that daily mobility of people and real data from the 2010 dengue outbreak in Hermosillo, Mexico. Based on a preliminary cluster analysis, we divide the city into two regions, the south and north sides, which determine each patch of the model. We use a Bayesian approach to estimate the transmission rates and local basic reproductive numbers of some urban mobility scenarios where residents of each patch spend daily the 100% (no human movement between patches), 75% and 50% of their day at their place of residence. For the north side, estimates of transmission rates do not vary and it is more likely that the local basic reproductive number to be greater than one for all three different scenarios. On the contrary, tranmission rates of the south side have more weight in lower values when consider the human movement between patches compared to the uncoupled case. In fact, local basic reproductive numbers less than 1 are not negligible for the south side. If information about commuting is known, this work might be useful to obtain better estimates of some contagion local properties of a patch, such as the basic reproductive number.

Lockdown and social distancing measures have been implemented for many countries to mitigate the impacts of the COVID-19 pandemic and prevent overwhelming of health services. However, success on this strategy depends not only on the timing of its implementation, but also on the relaxation measures adopted within each community. At the request of Sonoran Health Ministry, we developed a mathematical model to evaluate the impacts of the lockdown implemented in Hermosillo, Mexico. We compared this intervention with some hypothetical ones, varying the starting date and also the population proportion that is released, breaking the confinement. For this purpose, a Monte Carlo study was performed by considering three scenarios to define our baseline dynamics. Results showed that a hypothetical delay of two weeks, on the lockdown measures, would result in an early ACME around May 9 for hospitalization prevalence and an increase on cumulative deaths, 42 times higher by May 31, when compared to baseline. On the other hand, in respect of relaxation dynamics, the ACME levels depend on the proportion of people who gets back to daily activities or the individual behavior regarding prevention measures. It is important to stress that, according to information provided by health authorities, the ACME occurring time was closed to the one given by our model. Hence, we considered that our model resulted useful for the decision-making assessment, and that an extension of it can be used for the study of a potential second wave.

Lockdown and social distancing measures have been implemented for many countries to mitigate the impacts of the COVID-19 pandemic and prevent overwhelming of health services. However, success on this strategy depends not only on the timing of its implementation, but also on the relaxation measures adopted within each community. We developed a mathematical model to evaluate the impacts of the lockdown implemented in Hermosillo, Mexico. We compared this intervention with some hypothetical ones, varying the starting date and also the population proportion that is released, breaking the confinement. A Monte Carlo study was performed by considering three scenarios to define our baseline dynamics. Results showed that a hypothetical delay of two weeks, on the lockdown measures, would result in an early acme around May 9 for hospitalization prevalence and an increase on cumulative deaths, 42 times higher by May 31, when compared to baseline. On the other hand, results concerning relaxation dynamics showed that the acme levels depend on the proportion of people who gets back to daily activities as well as the individual behavior with respect to prevention measures. Analysis regarding different relaxing mitigation measures were provided to the Sonoran Health Ministry, as requested. It is important to stress that, according to information provided by health authorities, the acme occurring time was closed to the one given by our model. Hence, we considered that our model resulted useful for the decision-making assessment, and that an extension of it can be used for the study of a potential second wave.

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