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Register a new userApplication of Mathematical Epidemiology to crop vector-borne diseases. The cassava mosaic virus disease case
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In this chapter, an application of Mathematical Epidemiology to crop vector-borne diseases is presented to investigate the interactions between crops, vectors, and virus. The main illustrative example is the cassava mosaic disease (CMD). The CMD virus has two routes of infection: through vectors and also through infected crops. In the field, the main tool to control CMD spreading is roguing. The presented biological model is sufficiently generic and the same methodology can be adapted to other crops or crop vector-borne diseases. After an introduction where a brief history of crop diseases and useful information on Cassava and CMD is given, we develop and study a compartmental temporal model, taking into account the crop growth and the vector dynamics. A brief qualitative analysis of the model is provided,i.e., existence and uniqueness of a solution,existence of a disease-free equilibrium and existence of an endemic equilibrium. We also provide conditions for local (global) asymptotic stability and show that a Hopf Bifurcation may occur, for instance, when diseased plants are removed. Numerical simulations are provided to illustrate all possible behaviors. Finally, we discuss the theoretical and numerical outputs in terms of crop protection.
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In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called textit{level of abstraction} used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online.
The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening societies, governments have drawn insights from mathematical models of the spread of infectious diseases. In this article, we give an introduction to a family of mathematical models (called compartmental models) and discuss how the results of analyzing these models influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of the disease.
This paper describes a mathematical model for the spread of a virus through an isolated population of a given size. The model uses three, color-coded components, called molecules (red for infected and still contagious; green for infected, but no longer contagious; and blue for uninfected). In retrospect, the model turns out to be a digital analogue for the well-known SIR model of Kermac and McKendrick (1927). In our RGB model, the number of accumulated infections goes through three phases, beginning at a very low level, then changing to a transition ramp of rapid growth, and ending in a plateau of final values. Consequently, the differential change or growth rate begins at 0, rises to a peak corresponding to the maximum slope of the transition ramp, and then falls back to 0. The properties of these time variations, including the slope, duration, and height of the transition ramp, and the width and height of the infection rate, depend on a single parameter - the time that a red molecule is contagious divided by the average time between collisions of the molecules. Various temporal milestones, including the starting time of the transition ramp, the time that the accumulating number of infections obtains its maximum slope, and the location of the peak of the infection rate depend on the size of the population in addition to the contagious lifetime ratio. Explicit formulas for these quantities are derived and summarized. Finally, Appendix E has been added to describe the effect of vaccinations.
This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of susceptible-exposed-infectious-recovered model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran and Brazil. Afterward, numerical simulations are performed to analyzed different scenarios of COVID-19 in Brazil. Results show the importance of governmental and individual actions to control the number and the period of the critical situations related to the pandemic.
The goal of this note is to present a simple mathematical model with two parameters for the number of deaths due to the corona (COVID-19) virus. The model only requires basic knowledge in differential calculus, and can also be understood by pupils attending secondary school. The model can easily be implemented on a computer, and we will illustrate it on the basis of case studies for different countries.
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