اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA simple mathematical model for the evolution of the corona virus
354
0
0.0
(
0
)
تأليف
Stefan Tappe
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 long
er 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.
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 viru
s 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.
Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compa
rtmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a real-world disease. Different models of disease including the SIR, SIRm and SEIR model are compared with respect to their ability to predict disease spread. Physical distancing impacts and personal protection equipment use will be discussed in relevance to the COVID-19 spread.
Malaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year. In this paper, we develop a model for allocating malaria interventions across geographic regions and time, subject to budget constr
aints, with the aim of minimizing the number of person-days of malaria infection. The model considers a range of several conditions: climatic characteristics, treatment efficacy, distribution costs, and treatment coverage. We couple an expanded susceptible-infected-recovered (SIR) compartment model for the disease dynamics with an integer linear programming (ILP) model for selecting the disease interventions. Our model produces an intervention plan for all regions, identifying which combination of interventions, with which level of coverage, to use in each region and year in a five-year planning horizon. Simulations using the model yield high-level, qualitative insights on optimal intervention policies: The optimal policy is different when considering a five-year time horizon than when considering only a single year, due to the effects that interventions have on the disease transmission dynamics. The vaccine intervention is rarely selected, except if its assumed cost is significantly lower than that predicted in the literature. Increasing the available budget causes the number of person-days of malaria infection to decrease linearly up to a point, after which the benefit of increased budget starts to taper. The optimal policy is highly dependent on assumptions about mosquito density, selecting different interventions for wet climates with high density than for dry climates with low density, and the interventions are found to be less effective at controlling malaria in the wet climates when attainable intervention coverage is 60% or lower. However, when intervention coverage of 80% is attainable, then malaria prevalence drops quickly.
The evolutionary dynamics of human Influenza A virus presents a challenging theoretical problem. An extremely high mutation rate allows the virus to escape, at each epidemic season, the host immune protection elicited by previous infections. At the s
ame time, at each given epidemic season a single quasi-species, that is a set of closely related strains, is observed. A non-trivial relation between the genetic (i.e., at the sequence level) and the antigenic (i.e., related to the host immune response) distances can shed light into this puzzle. In this paper we introduce a model in which, in accordance with experimental observations, a simple interaction rule based on spatial correlations among point mutations dynamically defines an immunity space in the space of sequences. We investigate the static and dynamic structure of this space and we discuss how it affects the dynamics of the virus-host interaction. Interestingly we observe a staggered time structure in the virus evolution as in the real Influenza evolutionary dynamics.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
