Analysis of a Simple HIV/TB Coinfection Model with the Effect of Scree
Anne George, K. S. Joshy, Mathew Sebastian, Oluwatobi Samuel Oluwafemi, Sabu Thomas in Holistic Approaches to Infectious Diseases, 2017
The parameters used in this model are as follows: Λ is the recruitment rate constant; α is the fraction of total HIV/AIDS infected individuals who are screened and are under proper counseling; η is the fraction of total TB infected individuals who are screened; ν is recovery rate of detected TB patients; μ is the natural death rate constant; β1 is the rate of TB transmission, β2 is the rate of HIV transmission; 1 is TB related death rate; β2 is HIV/AIDS related death rate; β3 is the death rate constant of co-infected individuals. Here all the parameters of the model are non-negative and it is noted that the rate of transmission of tuberculosis, i.e., β1 is greater than the rate of transmission of HIV i.e., 2 The region of attraction of this model is given by D = {} and the solutions S(t),I1(t),I2(t) and I3(t) of the system (2.1) remains posi-tively invariant. The transfer diagram of the model is described in Figure 6.1. The Basic reproduction number corresponding to TB and HIV are computed as R1 =, respectively. The basic reproduction number is nothing but the number of new cases (infectives) generated from a single infective in his/her whole infectious period. And in general if this number is less than one then disease automatically dies out.
And Now, as Promised
Rae-Ellen W. Kavey, Allison B. Kavey in Viral Pandemics, 2020
Crucial findings with any new disease include the range of clinical severity, the extent of transmission and rates of infection – all remained unknown at this stage despite more than 71,000 cases of COVID-19 and 1600 deaths, as of February 17, 2020. The virus spreads both directly – through physical transfer between people through close contact with oral or nasal secretions – and indirectly, through contact with droplets deposited on nearby surfaces when an infected person coughs or sneezes, which can then be carried to the eyes, nose or mouth of a healthy subject. We do know that 2019-nCoV/ SARS-CoV-2 is too big to stay suspended in the air for any significant length of time or to travel more than a few feet and this should limit transmission. As with SARS, droplets generated during medical procedures can be aerosolized, augmenting the potential for infection of healthcare providers. Hand hygiene for both infected and uninfected individuals and personal protective barriers – gowns, gloves, masks, and goggles – reduce droplet transmission. Estimates of the basic reproduction number or R0 for the virus – the number of additional persons one case infects over the course of their illness – have generally ranged from 2.2 to 3.6, but there are estimates as high as 6.5.13 (An R0 of less than 1 indicates very low transmission potential; the higher the R0, the greater the potential for sustained transmission. As an example, the R0 for measles is 18!)
Mathematical Modelling and Analysis of Fractional Epidemic Models Using Derivative with Exponential Kernel
Devendra Kumar, Jagdev Singh in Fractional Calculus in Medical and Health Science, 2020
By setting and , a simple calculation shows that the epidemic system seen in the previous section has a disease-free equilibrium state , which corresponds to the existence of population class of u only. We define the basic reproduction number as , where . If , we obtain a non-trivial state that corresponds to the existence of susceptible, infected and recovered individuals. This equilibrium state is denoted by
Fractional dynamics and stability analysis of COVID-19 pandemic model under the harmonic mean type incidence rate
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Amir Khan, Rahat Zarin, Saddam Khan, Anwar Saeed, Taza Gul, Usa Wannasingha Humphries
Keeping the above discussion in mind we formulated a covid 19 epidemic model and analyzed its different dynamics by considering the deterministic approach as well as fractional approach. The basic reproduction number is the threshold value that gives us information whether the disease spreads or not, as has been found by Next Generation Method. Covid 19 models under harmonic mean incidence rate have not given too much attention. Therefore we considered the harmonic mean type incidence rate and in the deterministic model, we established the local as well as the global stability for the said model. To minimize the infected people and maximize the susceptible people one can use optimal control theory by choosing suitable optimal control variables. For this, we used sensitivity analysis to highlight the most highly sensitive parameters which are useful in optimal control theory.
Positivity rate: an indicator for the spread of COVID-19
Published in Current Medical Research and Opinion, 2021
Ahmed Al Dallal, Usama AlDallal, Jehad Al Dallal
We define the basic reproduction number, R0, as the expected number of secondary infection cases caused by a primary infection case in a susceptible population32. During a pandemic, the corresponding factor is referenced as the effective reproduction number, Re, which is defined as the actual number of secondary infection cases caused by a primary infection case. At any point of time during a pandemic, the value of Re indicates whether the spread of the disease is speeding up (Re > 1) or slowing down (Re < 1). Some researchers suggest considering the value of Re when making lockdown and reopening decisions18. In addition, the change in Re values is considered to assess whether enforced precautionary measures in a certain country effectively reduce the spread of a disease19,33,34.
Estimation of the doubling time and reproduction number for COVID-19
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Shamim Ahmed, Mohammad Shemanto, Hasin Azhari, Golam Zakaria
The basic reproduction number or the reproduction number (R0) specifies the average number of the secondary infections caused by one infected individual during the entire infectious period at the start of an outbreak. The definition describes the state where all individuals are susceptible to infection and no other individuals are infected or immunized (naturally or through vaccination). It is one of the fundamental and most often used metrics for the study of infectious disease dynamics. An outbreak is expected to continue if R0 has a value > 1 and to end if R0 is < 1. The first modern application of R0 in epidemiology can be traced by the work of Macdonald (1952). Although MacDonald used Z0 to represent the metric and he called it basic reproduction rate. The use of the word rate suggests a quantity having a unit with a per-time dimension. If R0 were a rate involving time, the metric would provide information about how quickly an epidemic will spread through a population. But R0 does not indicate whether new cases will occur within a specific period of time. That is why calling R0 a rate rather than a number creates confusion. Throughout this paper, we refer this parameter reproduction number.
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