A mathematical model to describe antibody-dependent enhancement and assess the effect of limiting cloning for plasma cells in heterologous secondary dengue infection.

We propose a mathematical model to study the antibody-dependent enhancement (ADE) phenomenon. Here, we explore the interaction between macrophages, dengue virus and plasma cells, especially the effect of a limitation on plasma cell proliferation, which occurs due to immunological memory. The model has up to three equilibrium points: one virus-free equilibrium and two virus-presence equilibrium, depending on the value of two thresholds. We determine the existence regions for the model equilibrium points and their stability, a sensitivity analysis was performed in the model thresholds. Numerical simulations illustrate that ADE can occur even when the basic reproduction number is less than one.

Modeling the transmission of the new coronavirus in São Paulo State, Brazil-assessing the epidemiological impacts of isolating young and elder persons.

We developed a mathematical model to describe the new coronavirus transmission in São Paulo State, Brazil. The model divided a community into subpopulations composed of young and elder persons considering a higher risk of fatality among elder persons with severe CoViD-19. From the data collected in São Paulo State, we estimated the transmission and additional mortality rates. Based on the estimated model parameters, we calculated the basic reproduction number $R_{0}$, and we retrieved the number of deaths due to CoViD-19, which was three times lower than those found in the literature. Considering isolation as a control mechanism, we varied the isolation rates in the young and elder subpopulations to assess the epidemiological impacts. The epidemiological scenarios focused mainly on evaluating the reduction in the number of severe CoViD-19 cases and deaths due to this disease when isolation is introduced in a population.

Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue

Dengue is a vector-borne disease transmitted by the mosquito Aedes aegypti. The incidence of dengue disease shows a clear dependence on seasonal variation. How does the temperature affect the incidence? We addressed this question indirectly by estimating the size of the A. aegypti population for different temperatures applying population dynamics theory. In order to achieve this objective we designed temperature-controlled experiments to assess the entomological parameters regarding the mosquito's life-cycle at different temperatures. By obtaining the mortality, transition and oviposition rates for different stages of the life-cycle of the mosquito we were able to calculate the basic offspring number Q0, which is the capacity of vector reproduction and ultimately gives the size of the vector population...

Assessing the effects of temperature on dengue transmission

The incidence of dengue infection, a vector-borne disease transmitted by the mosquito Aedes aegypti, shows clear dependence on seasonal variation. Based on the quantification method that furnishes the size of the A. aegypti population in terms of the estimated entomological parameters for different temperatures, we assessed the risk of dengue outbreaks. The persistence and severity of epidemics can be assessed by the basic reproduction number R0, which varies with temperature. The expression for R0 obtained from ‘true’ and ‘pseudo’ mass action laws for dengue infection is discussed...

Estimación del número de reproducibilidad basal para la leishmaniasis tegumentar americana en dos localidades del nordeste de la Provincia de Salta, Argentina / Estimation of the basic reproducibility number for American tegumentary leishmaniasis in two sitesin northeastern Salta Province, Argentina

Un modelo matemático determinístico del tipo SIR para tres hospedadores es aplicado para analizar el proceso de transmisión de la leishmaniasis tegumentar americana, en las localidades Río Blanco y paraje Las Carmelitas, ubicadas en el Nordeste de la Provincia de Salta, Argentina, del mismo se deriva la expresión para el número de reproducibilidad basal Ro. Se implementa el modelo en ambiente MATLAB, en base a datos de las zonas endémicas se realizan simulaciones y se obtienen estimaciones numéricas de Ro. Para el caso de Río Blanco hemos obtenido el valor Ro = 4,689, mientras que para el paraje Las Carmelitas se obtuvo Ro = 1,948. Estudiando numéricamente el modelo también se estima la fuerza de infección, obteniendo para las localidades mencionadas 0,239 y 0,171 (unidad 1/año), respectivamente. Las simulaciones muestran que en la localidad de Río Blanco la fase endémica resulta más sostenida que la fase inter-epidémica presentada en el paraje Las Carmelitas. Las estimaciones obtenidas para estos parámetros epidemiológicos indican donde las instituciones del Ministerio de Salud Pública de la Provincia y de la Nación tendrán más dificultad para el control y la erradicación de la enfermedad.

A SIR-type deterministic mathematical model for three hosts is applied to analyze the transmission process for American tegumentary leishmaniasis in Río Blanco and Las Carmelitas, located in northeastern Salta Province, Argentina, and to derive the expression for the baseline reproducibility number Ro. The model is implemented in the MATLAB environment, and based on data from endemic areas, simulations are performed and numerical estimations of Ro are obtained. Río Blanco shows Ro = 4.689 and Las Carmelitas Ro = 1.948. By studying the model numerically, we also estimate the force of infection, namely 0.239 and 0.171 (unit 1/year), respectively. The simulations show that in Río Blanco, the endemic phase was more sustained than the inter-epidemic phase in Las Carmelitas. The estimations of these epidemiological parameters indicate where the Ministry of Health and Provincial Health Department will experience greater difficulty in controlling and eradicating the disease.

Modelagem matemática do fator de risco da leishmaniose canina na leishmaniose humana em regiões oeste do Estado de São Paulo, Brasil, e noroeste da província de Salta, Argentina / Mathematical modeling of the risk factores for canine leishmaniosis in human leishmaniosis in western regions of the state of São Paulo, Brazil, and in the northeastern of the province of Salta, Argentina

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Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique.

We propose a mathematical model to assess the effects of irradiated (or transgenic) male insects introduction in a previously infested region. The release of sterile male insects aims to displace gradually the natural (wild) insect from the habitat. We discuss the suitability of this release technique when applied to peri-domestically adapted Aedes aegypti mosquitoes which are transmissors of Yellow Fever and Dengue disease.