scholarly journals Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects

2008 ◽  
Vol 13 (3) ◽  
pp. 331-350 ◽  
Author(s):  
Ram Naresh ◽  
Surabhi Pandey ◽  
A. K. Misra
Keyword(s):  
Infectious Diseases ◽  
Logistic Model ◽  
Reproduction Number ◽  
Size Structure ◽  
Backward Bifurcation ◽  
Threshold Condition ◽  
Nonlinear Mathematical Model ◽  
Variable Size ◽  
Carrier Population

We have proposed and analyzed a nonlinear mathematical model for the spread of carrier dependent infectious diseases in a population with variable size structure including the role of vaccination. It is assumed that the susceptibles become infected by direct contact with infectives and/or by the carrier population present in the environment. The density of carrier population is assumed to be governed by a generalized logistic model and is dependent on environmental and human factors which are conducive to the growth of carrier population. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccine induced reproduction number R(φ) which is, if less than one, the disease dies out in the absence of carriers provided the vaccine efficacy is high enough, and otherwise the infection is maintained in the population. The model also exhibits backward bifurcation at R(φ) = 1. It is also shown that the spread of an infectious disease increases as the carrier population density increases. In addition, the constant immigration of susceptibles makes the disease more endemic.

MATHEMATICAL MODELING AND ANALYSIS OF THE SPREAD OF CARRIER DEPENDENT INFECTIOUS DISEASES: EFFECTS OF CUMULATIVE DENSITY OF ENVIRONMENTAL FACTORS

2009 ◽  
Vol 02 (02) ◽  
pp. 213-228 ◽  
Author(s):  
SHIKHA SINGH ◽  
J. B. SHUKLA ◽  
PEEYUSH CHANDRA
Keyword(s):  
Environmental Factors ◽  
Infectious Diseases ◽  
Logistic Model ◽  
Cumulative Effect ◽  
Population Increase ◽  
Growth Equation ◽  
Nonlinear Mathematical Model ◽  
Modeling And Analysis ◽  
Dependent Growth ◽  
Carrier Population

In this paper, a nonlinear mathematical model with immigration for carrier dependent infectious diseases is proposed and analyzed by considering explicitly the cumulative effect of environmental factors, which are conducive to the growth of carrier population. It is assumed that the density of carrier population is governed by a general logistic model. It is assumed further that the growth rate per capita and the modified carrying capacity of carrier population increase as the cumulative density of environmental factors, governed by population density dependent growth equation, increases. It is shown that as the parameters governing environmental factors increase, the number of infectives in the population increases. It is also found that due to immigration, the disease becomes more endemic.

Modelling the role of opportunistic diseases in coinfection

2018 ◽  
Vol 13 (3) ◽  
pp. 28
Author(s):  
Marcos Marvá ◽  
Rafael Bravo de la Parra ◽  
Ezio Venturino
Keyword(s):  
Epidemic Model ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Rate ◽  
Opportunistic Disease ◽  
Sis Epidemic Model ◽  
Primary Disease ◽  
Sis Epidemic

In this paper, we formulate a model for evaluating the effects of an opportunistic disease affecting only those individuals already infected by a primary disease. The opportunistic disease act on a faster time scale and it is represented by an SIS epidemic model with frequency-dependent transmission. The primary disease is governed by an SIS epidemic model with density-dependent transmission, and we consider two different recovery cases. The first one assumes a constant recovery rate whereas the second one takes into account limited treatment resources by means of a saturating treatment rate. No demographics is included in these models.Our results indicate that misunderstanding the role of the opportunistic disease may lead to wrong estimates of the overall potential amount of infected individuals. In the case of constant recovery rate, an expression measuring this discrepancy is derived, as well as conditions on the opportunistic disease imposing a coinfection endemic state on a primary disease otherwise tending to disappear. The case of saturating treatment rate adds the phenomenon of backward bifurcation, which fosters the presence of endemic coinfection and greater levels of infected individuals. Nevertheless, there are specific situations where increasing the opportunistic disease basic reproduction number helps to eradicate both diseases.

MODELING THE ROLE OF DISSOLVED OXYGEN-DEPENDENT BACTERIA ON BIODEGRADATION OF ORGANIC POLLUTANTS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450008 ◽  
Author(s):  
J. B. SHUKLA ◽  
ASHISH GOYAL ◽  
P. K. TIWARI ◽  
A. K. MISRA
Keyword(s):  
Dissolved Oxygen ◽  
Water Body ◽  
Logistic Model ◽  
Simulation Analysis ◽  
Organic Pollutant ◽  
The Other ◽  
Nonlinear Mathematical Model ◽  
The Stability ◽  
The One

In this paper, a nonlinear mathematical model is proposed and analyzed to study the role of dissolved oxygen (DO)-dependent bacteria on biodegradation of one or two organic pollutant(s) in a water body. In the case of two organic pollutant(s), it is assumed that the one is fast degrading and the other is slow degrading and both are discharged into the water body from outside with constant rates. The density of bacteria is assumed to follow logistic model and its growth increases due to biodegradation of one or two organic pollutant(s) as well as with the increase in the concentration of DO. The model is analyzed using the stability theory of differential equations and by simulation. The model analysis shows that the concentration(s) of one or both organic pollutant(s) decrease(s) as the density of bacteria increases. It is noted that for very large density of bacteria, the organic pollutant(s) may be removed almost completely from the water body. It is found that simulation analysis confirms the analytical results. The results obtained in this paper are in line with the experimental observations published in literature.

Modeling and Analysis of the Spread of Carrier Dependent Infectious Diseases with Environmental Effects

2003 ◽  
Vol 11 (03) ◽  
pp. 325-335 ◽  
Author(s):  
Shikha Singh ◽  
Peeyush Chandra ◽  
J. B. Shukla
Keyword(s):  
Population Density ◽  
Infectious Diseases ◽  
Logistic Model ◽  
Human Population ◽  
Population Increase ◽  
Related Factors ◽  
Modeling And Analysis ◽  
Modeling Process ◽  
Per Capita ◽  
Carrier Population

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

scholarly journals Complex Dynamics of An Epidemic Model With Saturated Media Coverage and Recovery

2021 ◽  
Author(s):  
Tangjuan Li ◽  
Yanni Xiao
Keyword(s):  
Infectious Diseases ◽  
Disease Transmission ◽  
Media Coverage ◽  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Emerging Infectious Diseases ◽  
Backward Bifurcation ◽  
Threshold Condition ◽  
Medical Resources ◽  
Saturated Media

Abstract During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically obtained that saturated recovery significantly contributes the occurrence of backward bifurcation and rich dynamics. Then it is reasonable to only considering nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. And numerical simulations reveals the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, Saddle-Node bifurcation, Homoclinic bifurcation and unstable limit cycle. Comparing the system with linear recovery, where the threshold dynamic are almost completely characterized by a threshold condition called the basic reproduction number, we concluded that only saturated media impact hardly induces the complicated dynamics, while the nonlinear recovery function, associated with limitation of medical resources, may induce the coexistence of the disease-free equilibrium (DFE) and a endemic state or multiple endemic states, which means that the limitation of medical resources causes much difficulties in eliminating the infectious diseases.

scholarly journals Modelling the Potential Role of Media Campaigns in Ebola Transmission Dynamics

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Sylvie Diane Djiomba Njankou ◽  
Farai Nyabadza
Keyword(s):  
Local Stability ◽  
Potential Role ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
Media Campaigns ◽  
Disease States ◽  
The Media ◽  
The Stability

A six-compartment mathematical model is formulated to investigate the role of media campaigns in Ebola transmission dynamics. The model includes tweets or messages sent by individuals in different compartments. The media campaigns reproduction number is computed and used to discuss the stability of the disease states. The presence of a backward bifurcation as well as a forward bifurcation is shown together with the existence and local stability of the endemic equilibrium. Results show that messages sent through media have a more significant beneficial effect on the reduction of Ebola cases if they are more effective and spaced out.

Treatment of ebola and other infectious diseases: melatonin “goes viral”

2020 ◽  
Vol 3 (1) ◽  
pp. 43-57 ◽  
Author(s):  
Russel J Reiter ◽  
Qiang Ma ◽  
Ramaswamy Sharma
Keyword(s):  
Mortality Rate ◽  
Infectious Diseases ◽  
Hemorrhagic Shock ◽  
Safety Profile ◽  
Ebola Virus ◽  
Viral Infections ◽  
Virus Disease ◽  
Attractive Potential ◽  
Potential Treatment

This review summarizes published reports on the utility of melatonin as a treatment for virus-mediated diseases. Of special note are the data related to the role of melatonin in influencing Ebola virus disease. This infection and deadly condition has no effective treatment and the published works documenting the ability of melatonin to attenuate the severity of viral infections generally and Ebola infection specifically are considered. The capacity of melatonin to prevent one of the major complications of an Ebola infection, i.e., the hemorrhagic shock syndrome, which often contributes to the high mortality rate, is noteworthy. Considering the high safety profile of melatonin, the fact that it is easily produced, inexpensive and can be self-administered makes it an attractive potential treatment for Ebola virus pathology.  

scholarly journals Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ganna Rozhnova ◽  
Christiaan H. van Dorp ◽  
Patricia Bruijning-Verhagen ◽  
Martin C. J. Bootsma ◽  
Janneke H. H. M. van de Wijgert ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Additional Benefit ◽  
Transmission Model ◽  
Time Points ◽  
School Based ◽  
Admission Data ◽  
Age Structured ◽  
The Impact ◽  
Pandemic Wave

AbstractThe role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We use an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

scholarly journals MicroRNAs: Biological Regulators in Pathogen–Host Interactions

Cells ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 113 ◽  
Author(s):  
Stephanie Maia Acuña ◽  
Lucile Maria Floeter-Winter ◽  
Sandra Marcia Muxel
Keyword(s):  
Immune Response ◽  
Infectious Diseases ◽  
Small Rnas ◽  
Immune Cell ◽  
Fine Tuning ◽  
Biological Processes ◽  
Host Interactions ◽  
The Past ◽  
Biological Aspects

An inflammatory response is essential for combating invading pathogens. Several effector components, as well as immune cell populations, are involved in mounting an immune response, thereby destroying pathogenic organisms such as bacteria, fungi, viruses, and parasites. In the past decade, microRNAs (miRNAs), a group of noncoding small RNAs, have emerged as functionally significant regulatory molecules with the significant capability of fine-tuning biological processes. The important role of miRNAs in inflammation and immune responses is highlighted by studies in which the regulation of miRNAs in the host was shown to be related to infectious diseases and associated with the eradication or susceptibility of the infection. Here, we review the biological aspects of microRNAs, focusing on their roles as regulators of gene expression during pathogen–host interactions and their implications in the immune response against Leishmania, Trypanosoma, Toxoplasma, and Plasmodium infectious diseases.

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