Related Papers
Sains Malaysiana
Mathematical Model of Dengue Virus with Predator-Prey Interactions
2020 •
Sarinah Siddik
In this paper, a mathematical model of dengue incorporating two sub-models that: describes the linked dynamics between predator-prey of mosquitoes at the larval stage, and describes the dengue spread between humans and adult mosquitoes, is formulated to simulate the dynamics of dengue spread. The effect of predator-prey dynamics in controlling the dengue disease at the larval stage of mosquito populations is investigated. Stability analysis of the equilibrium points are carried out. Numerical simulations results indicate that the use of predator-prey dynamics of mosquitoes at the larval stage as biological control agents for controlling the larval stage of dengue mosquito assists in combating dengue virus contagion.
Journal of Mathematical Analysis and Applications
On the dynamics of a class of multi-group models for vector-borne diseases
2016 •
Gauthier Sallet
Memorias Do Instituto Oswaldo Cruz
Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil
2003 •
Eduardo Massad
Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.
TENTH INTERNATIONAL CONFERENCE DYNAMICAL SYSTEMS APPLIED TO BIOLOGY AND NATURAL SCIENCES (DSABNS)
Adapted Numerical Methods for Advection Diffusion Problems
2019 •
Dajana Conte
Journal of Biological Systems
Modeling Zika Transmission Dynamics: Prevention and Control
Ranjit Kumar Upadhyay
The Zika virus (ZIKV) epidemic is depicted to have high spatial diversity and slow growth, attributable to the dynamics of the mosquito vector and mobility of the human populations. In an effort to understand the transmission dynamics of Zika virus, we formulate a new compartmental epidemic model with a system of seven differential equations and 11 parameters incorporating the decaying transmission rate and study the impact of protection measure on basic public health. We do not fit the model to the observed pattern of spread, rather we use parameter values estimated in the past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Brazil, via reaction–diffusion modeling. Our work includes estimation of key epidemiological parameters such as basic reproduction number ([Formula: see text], and gives a rough estimate of how many individuals can be typically infected during an outbreak if it occurs in India. We used partial rank correla...
Journal of Medical Entomology
Can Horton Hear the Whos? The Importance of Scale in Mosquito-Borne Disease
2014 •
Stephanie Richards
Journal of Mathematical Analysis and Applications
On the solutions and conservation laws of the model for tumor growth in the brain
2009 •
F.D. Zaman
Annals of the Entomological Society of America
Human–Mosquito Contact: A Missing Link in Our Understanding of Mosquito-Borne Disease Transmission Dynamics
2021 •
Durrell Kapan
Despite the critical role that contact between hosts and vectors, through vector bites, plays in driving vector-borne disease (VBD) transmission, transmission risk is primarily studied through the lens of vector density and overlooks host–vector contact dynamics. This review article synthesizes current knowledge of host–vector contact with an emphasis on mosquito bites. It provides a framework including biological and mathematical definitions of host–mosquito contact rate, blood-feeding rate, and per capita biting rates. We describe how contact rates vary and how this variation is influenced by mosquito and vertebrate factors. Our framework challenges a classic assumption that mosquitoes bite at a fixed rate determined by the duration of their gonotrophic cycle. We explore alternative ecological assumptions based on the functional response, blood index, forage ratio, and ideal free distribution within a mechanistic host–vector contact model. We highlight that host–vector contact is ...
Predators indirectly control vector- borne disease: linking predator prey and host -pathogen models
2009 •
Bernard K Mutuku
