Abstract: Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible-Infectious-Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

Abstract: Malaria remains a major health problem in many parts of the world, including Sub-Saharan Africa. Insecticide-treated nets, in combination with other control measures, have been effective in reducing malaria incidence over the past two decades. Nevertheless, there are concerns about improper handling and misuse of nets, producing possible health effects from intoxication and collateral environmental damage. The latter is caused, for instance, from artisanal fishing. We formulate a model of impulsive differential equations to describe the interplay between malaria dynamics, human intoxication, and ecosystem damage; affected by human awareness to these risks and levels of net usage. Our results show that an increase in mosquito net coverage reduces malaria prevalence and increases human intoxications. In addition, a high net coverage significantly reduces the risk perception to disease, naturally increases the awareness for intoxications from net handling, and scarcely increases the risk perception to collateral damage from net fishing. According to our model, campaigns aiming at reducing disease prevalence or intoxications are much more successful than those creating awareness to ecosystem damage. Furthermore, we can observe from our results that introducing closed fishing periods reduces environmental damage more significantly than strategies directed towards increasing the risk perception for net fishing.

Abstract: Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.

Abstract: ince the detection of the first case of COVID-19 in Chile on March 3(rd), 2020, a total of 513,188 cases, including similar to 14,302 deaths have been reported in Chile as of November 2(nd), 2020. Here, we estimate the reproduction number throughout the epidemic in Chile and study the effectiveness of control interventions especially the effectiveness of lockdowns by conducting short-term forecasts based on the early transmission dynamics of COVID-19. Chile's incidence curve displays early sub-exponential growth dynamics with the deceleration of growth parameter, p, estimated at 0.8 (95% CI: 0.7, 0.8) and the reproduction number, R, estimated at 1.8 (95% CI: 1.6, 1.9). Our findings indicate that the control measures at the start of the epidemic significantly slowed down the spread of the virus. However, the relaxation of restrictions and spread of the virus in low-income neighborhoods in May led to a new surge of infections, followed by the reimposition of lockdowns in Greater Santiago and other municipalities. These measures have decelerated the virus spread with R estimated at similar to 0.96 (95% CI: 0.95, 0.98) as of November 2(nd), 2020. The early sub-exponential growth trend (p similar to 0.8) of the COVID-19 epidemic transformed into a linear growth trend (p similar to 0.5) as of July 7(th), 2020, after the reimposition of lockdowns. While the broad scale social distancing interventions have slowed the virus spread, the number of new COVID-19 cases continue to accrue, underscoring the need for persistent social distancing and active case detection and isolation efforts to maintain the epidemic under control.
Author summary
In context of the ongoing COVID-19 pandemic, Chile has been one of the hardest-hit countries in Latin America, struggling to contain the spread of the virus. In this manuscript, we employ renewal equation to estimate the reproduction number (R) for the early ascending phase of the COVID-19 epidemic and by July 7(th), 2020 to guide the magnitude and intensity of interventions required to combat the COVID-19 epidemic. We also estimate the instantaneous reproduction number throughout the epidemic in Chile. Moreover, we generate short-term forecasts based on the epidemic trajectory using phenomenological models, and assess counterfactual scenarios to understand any additional resources required to contain the virus' spread. Our results indicate early sustained transmission of SARS-CoV-2. However, the initial control measures at the start of the epidemic significantly slowed down the spread of the virus. The easing of COVID-19 restrictions in April led to a new wave of infections, followed by the re-imposition of lockdowns in Greater Santiago and several municipalities. Most recent estimates of reproduction number indicate a decline in the virus transmission. While broad-scale social distancing interventions have slowed the virus spread, the number of new COVID-19 cases continue to accrue, underscoring the need for persistent social distancing efforts.

Abstract: A deterministic model for the effects on disease prevalence of the most advanced preerythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector-host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number R and establish conditions for the existence and stability of equilibria to the system. The model is bistable when R < 1. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that R = 1 is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce R to a value smaller than unity. Therefore, it is crucial to be cautious when using R to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules.