scholarly journals Transmission Dynamics of Lymphatic Filariasis: A Mathematical Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
C. P. Bhunu ◽  
S. Mushayabasa
Keyword(s):  
Numerical Simulations ◽  
Lymphatic Filariasis ◽  
Reproduction Number ◽  
Epidemiological Model ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Mathematical Approach

An epidemiological model for the spread of lymphatic filariasis, a mosquito-borne infection, is developed and analysed. The epidemic thresholds known as the reproduction number and equilibria for the model are determined and stabilities analysed. Results from the analysis of the reproduction number suggest that treatment will somehow contribute to a reduction in lymphatic filariasis cases, but what it does not show is the magnitude of the reduction, a part answered by the numerical simulations. Numerical simulations show that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms as well as chemoprophylaxis for the exposed.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Lymphatic Filariasis Model with Prevention and Treatment in Human Under Treatment Barriers

2020 ◽  
pp. 280-292
Author(s):  
Aziza J. Iddi
Keyword(s):  
Lymphatic Filariasis ◽  
Preventive Measures ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Treatment Barriers ◽  
Treatment Intervention ◽  
Prevention And Treatment ◽  
The Impact ◽  
Disease Free ◽  
Disease Persistence

In this paper, a deterministic Lymphatic Filariasis (LF) model with preventive measures in human and treatment barriers is developed and analysed to assess the impact of treatment barriers on the transmission dynamics of LF in endemic areas. Qualitative analysis and numerical simulation are presented in terms of the reproduction number of the model in the absence and presence of treatment barriers. It is established that the treatment intervention has shown improvement in the reduction of LF infection in the population. Furthermore, in the absence of treatment barriers the model guaranteed disease extinction behaviour, while in the presence of treatment barriers the model shows disease persistence behaviour when . This means that in the presence of treatment barriers there is coexistence of the stable disease-free state and the stable persistent state of the disease when . The persistence behaviour may be due to plentiful infected individuals who accumulate in the community due to treatment barriers while the disease has no natural recovery. The numerical simulations are performed to complement the analytical results.

scholarly journals A Data Driven Analysis and Forecast of COVID-19 Dynamics during the Third Wave Using SIRD Model in Bangladesh

COVID ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 503-517
Author(s):  
Omar Faruk ◽  
Suman Kar
Keyword(s):  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Goodness Of Fit ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Third Wave ◽  
The Third ◽  
The Government ◽  
The Basic Reproduction Number

In this study, we developed a compartmental SIRD model to analyze and forecast the transmission dynamics of the COVID-19 pandemic in Bangladesh during the third wave caused by the Indian delta variant. With the help of the nonlinear system of differential equations, this model can analyze the trends and provide reliable predictions regarding how the epidemic would evolve. The basic reproduction number regarding the pandemic has been determined analytically. The parameters used in this model have been estimated by fitting our model to the reported data for the months of May, June, and July 2021 and the goodness of fit of the parameter’s value has been found by the respective regression coefficients. Further, we conducted a sensitivity analysis of the basic reproduction number and observed that decreasing the transmission rate is the most significant factor in disease prevention. Our proposed model’s appropriateness for the available COVID-19 data in Bangladesh has been demonstrated through numerical simulations. According to the numerical simulation, it is evident that a rise in the transmission rate leads to a significant increase in the infected number of the population. Numerical simulations have also been performed by using our proposed model to forecast the future transmission dynamics for COVID-19 over a longer period of time. Knowledge of these forecasts may help the government in adopting appropriate measures to prepare for unforeseen situations that may arise in Bangladesh as well as to minimize detrimental impacts during the outbreak.

scholarly journals A minimal model for household effects in epidemics

2020 ◽  
Author(s):  
Greg Huber ◽  
Mason Kamb ◽  
Kyle Kawagoe ◽  
Lucy Li ◽  
Boris Veytsman ◽  
...  
Keyword(s):  
Field Theory ◽  
Numerical Simulations ◽  
Minimal Model ◽  
Reproduction Number ◽  
Mean Field Theory ◽  
Mean Field ◽  
Household Size ◽  
Transmission Dynamics ◽  
Square Root ◽  
Close Contacts

Shelter-in-place and other confinement strategies implemented in the current COVID-19 pandemic have created stratified patterns of contacts between people: close contacts within households and more distant contacts between the households. The epidemic transmission dynamics is significantly modified as a consequence. We introduce a minimal model that incorporates these household effects in the framework of mean-field theory and numerical simulations. We show that the reproduction number R0 depends on the household size in a surprising way: linearly for relatively small households, and as a square root of size for larger households. We discuss the implications of the findings for the lockdown, test, tracing, and isolation policies.

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

2018 ◽  
Vol 11 (07) ◽  
pp. 1850092 ◽  
Author(s):  
A. Omame ◽  
R. A. Umana ◽  
D. Okuonghae ◽  
S. C. Inyama
Keyword(s):  
Human Papillomavirus ◽  
Numerical Simulations ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Effective Control ◽  
Male Population ◽  
Previous Infection ◽  
Males And Females ◽  
Parameter Values ◽  
The Impact

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease.

scholarly journals Modeling and reviewing analysis of the COVID-19 epidemic in Algeria with diagnostic shadow

2021 ◽  
Author(s):  
Jiwei Jia ◽  
Siyu Liu ◽  
Yawen Liu ◽  
Ruitong Shan ◽  
Khaled Zennir ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Effective Control ◽  
Reproduction Numbers ◽  
Epidemic Dynamic ◽  
Reported Data ◽  
Parameter Values ◽  
Research Period

In this paper, we formulate a special epidemic dynamic model to describe the transmission of COVID-19 in Algeria. We derive the threshold parameter control reproduction number (R0c ), and present the effective control reproduction number (Rc(t)) as a real-time index for evaluating the epidemic under different control strategies. Due to the limitation of the reported data, we redefine the number of accumulative confirmed cases with diagnostic shadow and then use the processed data to do the optimal numerical simulations. According to the control measures, we divide the whole research period into six stages. And then the corresponding medical resource estimations and the average effective control reproduction numbers for each stage are given. Meanwhile, we use the parameter values which are obtained from the optimal numerical simulations to forecast the whole epidemic tendency under different control strategies.

scholarly journals Can medication mitigate the need for a strict lock down?: A mathematical study of control strategies for COVID-19 infection

2020 ◽  
Author(s):  
Mohsin Ali ◽  
Mudassar Imran ◽  
Adnan Khan
Keyword(s):  
Reproduction Number ◽  
Virus Disease ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Mathematical Study ◽  
Seir Model ◽  
Epidemic Curve ◽  
Asymptomatic Individuals ◽  
Over Time

AbstractWe formulate a deterministic epidemic model to study the effects of medication on the transmission dynamics of Corona Virus Disease (COVID-19). We are especially interested in how the availability of medication could change the necessary quarantine measures for effective control of the disease. We model the transmission by extending the SEIR model to include asymptomatic, quarantined, isolated and medicated population compartments. We calculate the basic reproduction number R0 and show that for R0 < 1 the disease dies out and for R0 > 1 the disease is endemic. Using sensitivity analysis we establish that R0 is most sensitive to the rates of quarantine and medication. We also study how the effectiveness and the rate of medication along with the quarantine rate affect R0. We devise optimal quarantine, medication and isolation strategies, noting that availability of medication reduces the duration and severity of the lock-down needed for effective disease control. Our study also reinforces the idea that with the availability of medication, while the severity of the lock downs can be eased over time some social distancing protocols need to be observed, at least till a vaccine is found. We also analyze the COVID-109 outbreak data for four different countries, in two of these, India and Pakistan the curve is still rising, and in he other two, Italy and Spain, the epidemic curve is now falling due to effective quarantine measures. We provide estimates of R0 and the proportion of asymptomatic individuals in the population for these countries.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sahamoddin Khailaie ◽  
Tanmay Mitra ◽  
Arnab Bandyopadhyay ◽  
Marta Schips ◽  
Pietro Mascheroni ◽  
...  
Keyword(s):  
Structural Changes ◽  
Reproduction Number ◽  
National Level ◽  
Transmission Dynamics ◽  
Federal State ◽  
Parameter Estimates ◽  
Time Varying ◽  
Short Term ◽  
Robert Koch Institute ◽  
Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

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