scholarly journals A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda

2020 ◽  
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
Yahaya Gavamukulya ◽  
Richard Awichi ◽  
Peter Olupot–Olupot ◽  
Samson Rwahwire ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Transmission Rate ◽  
Control Strategies ◽  
Social Distancing ◽  
Corona Virus ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractThe human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.

scholarly journals Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

2021 ◽  
pp. 69-88
Author(s):  
Atokolo William ◽  
Omale David ◽  
Bashir Sezuo Tenuche ◽  
Olayemi Kehinde Samuel ◽  
Daniel Musa Alih ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measure ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Corona Virus ◽  
The Basic Reproduction Number

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

scholarly journals Role of Mathematical Model in Curbing COVID-19 in Nigeria

2021 ◽  
Vol 3 (2) ◽  
pp. 135-147
Author(s):  
Chinwendu Emilian Madubueze ◽  
Nkiru Maria Akabuike ◽  
Sambo Dachollom
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Viral Disease ◽  
Control Measures ◽  
Social Distancing ◽  
Testing Rate ◽  
Intervention Measures ◽  
The Impact ◽  
The Basic Reproduction Number

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

scholarly journals Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

The impact of media coverage with a piecewise transmission rate in the spread of diseases

2016 ◽  
Vol 10 (01) ◽  
pp. 1750003
Author(s):  
Maoxing Liu ◽  
Lixia Zuo
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Transmission ◽  
The Impact ◽  
The Basic Reproduction Number

A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.

scholarly journals Implications of the COVID-19 pandemic on eliminating trachoma as a public health problem

2020 ◽  
Author(s):  
Seth Blumberg ◽  
Anna Borlase ◽  
Joaquin M Prada ◽  
Anthony W Solomon ◽  
Paul Emerson ◽  
...  
Keyword(s):  
Public Health ◽  
Basic Reproduction Number ◽  
Health Problem ◽  
Reproduction Number ◽  
Control Strategies ◽  
Public Health Problem ◽  
New Paradigm ◽  
Specific Implementation ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractBackgroundProgress towards elimination of trachoma as a public health problem has been substantial, but the COVID-19 pandemic has disrupted community-based control efforts.MethodsWe use a susceptible-infected model to estimate the impact of delayed distribution of azithromycin treatment on the prevalence of active trachoma.ResultsWe identify three distinct scenarios for geographic districts depending on whether the basic reproduction number and the treatment-associated reproduction number are above or below a value of one. We find that when the basic reproduction number is below one, no significant delays in disease control will be caused. However, when the basic reproduction number is above one, significant delays can occur. In most districts a year of COVID-related delay can be mitigated by a single extra round of mass drug administration. However, supercritical districts require a new paradigm of infection control because the current strategies will not eliminate disease.ConclusionIf the pandemic can motivate judicious, community-specific implementation of control strategies, global elimination of trachoma as a public health problem could be accelerated.

scholarly journals Impact of Hygiene on Malaria Transmission Dynamics: A Mathematical Model

2021 ◽  
Author(s):  
Temidayo Oluwafemi ◽  
Emmanuel Azuaba
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Model System ◽  
Transmission Dynamics ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

Malaria continues to pose a major public health challenge, especially in developing countries, 219 million cases of malaria were estimated in 89 countries. In this paper, a mathematical model using non-linear differential equations is formulated to describe the impact of hygiene on Malaria transmission dynamics, the model is analyzed. The model is divided into seven compartments which includes five human compartments namely; Unhygienic susceptible human population, Hygienic Susceptible Human population, Unhygienic infected human population , hygienic infected human population and the Recovered Human population  and the mosquito population is subdivided into susceptible mosquitoes  and infected mosquitoes . The positivity of the solution shows that there exists a domain where the model is biologically meaningful and mathematically well-posed. The Disease-Free Equilibrium (DFE) point of the model is obtained, we compute the Basic Reproduction Number using the next generation method and established the condition for Local stability of the disease-free equilibrium, and we thereafter obtained the global stability of the disease-free equilibrium by constructing the Lyapunov function of the model system. Also, sensitivity analysis of the model system was carried out to identify the influence of the parameters on the Basic Reproduction Number, the result shows that the natural death rate of the mosquitoes is most sensitive to the basic reproduction number.

Theoretical assessment of the impact of environmental contamination on the dynamical transmission of polio

2019 ◽  
Vol 12 (02) ◽  
pp. 1950012 ◽  
Author(s):  
C. Balde ◽  
M. Lam ◽  
A. Bah ◽  
S. Bowong ◽  
J. J. Tewa
Keyword(s):  
Basic Reproduction Number ◽  
Environmental Contamination ◽  
Reproduction Number ◽  
Control Strategies ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Indirect Transmission ◽  
Populations At Risk ◽  
The Impact ◽  
The Basic Reproduction Number

A mathematical model for the dynamical transmission of polio is considered, with the aim of investigating the impact of environment contamination. The model captures two infection pathways through both direct human-to-human transmission and indirect human-to-environment-to-human transmission by incorporating the environment as a transition and/or reservoir of viruses. We derive the basic reproduction number [Formula: see text]. We show that the disease free equilibrium is globally asymptotically stable (GAS) if [Formula: see text], while if [Formula: see text], there exists a unique endemic equilibrium which is locally asymptotically stable (LAS). Similar results hold for environmental contamination free sub-model (without the incorporation of the indirect transmission). At the endemic level, we show that the number of infected individuals for the model with the environmental-related contagion is greater than the corresponding number for the environmental contamination free sub-model. In conjunction with the inequality [Formula: see text], where [Formula: see text] is the basic reproduction number for the environmental contamination free sub-model, our finding suggests that the contaminated environment plays a detrimental role on the transmission dynamics of polio disease by increasing the endemic level and the severity of the outbreak. Therefore, it is natural to implement control strategies to reduce the severity of the disease by providing adequate hygienic living conditions, educate populations at risk to follow rigorously those basic hygienic rules in order to avoid adequate contacts with suspected contaminated objects. Further, we perform numerical simulations to support the theory.

scholarly journals Modelling the Periodic Outbreak of Measles in Mainland China

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Control Strategies ◽  
Mainland China ◽  
Asymptomatic Infection ◽  
Protection Measures ◽  
The Basic Reproduction Number

In mainland China, measles infection reached the lowest level in 2012 but resurged again after that with a seasonally fluctuating pattern. To investigate the phenomenon of periodic outbreak and identify the crucial parameters that play in the transmission dynamics of measles, we formulate a mathematical model incorporating periodic transmission rate and asymptomatic infection with waning immunity. We define the basic reproduction number as the threshold value to govern whether measles infection dies out or not. Fitting the reported measles cases from 2013 to 2016 to our proposed model, we estimate the basic reproduction number R0 with immunization to be 1.0077. From numerical simulations, we conclude asymptomatic infection does not cause much new infections and the key parameters affecting the transmission of measles are vaccination rate, transmission rate, and recovery rate, which suggests the public to enhance vaccination and protection measures to reduce effective contacts between susceptible and infective individuals and treat infected individuals timely. To minimize the number of infected individuals at a minimal cost, we formulate an optimal control system to design optimal control strategies. Numerical simulations show the effectiveness of optimal control strategies and recommend us to implement the control strategies as soon as possible. In particular, enhancing vaccination is especially effective in lowering the initial outbreak and making disease recurrence less likely.

scholarly journals Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1564
Author(s):  
Gilberto Gonzalez-Parra ◽  
Abraham J. Arenas
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Potential Outcomes ◽  
Public Concern ◽  
Globally Asymptotically Stable ◽  
Lasalle Invariant Principle ◽  
The Mathematical Model ◽  
The Basic Reproduction Number

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

scholarly journals Mathematical Model of Schistosomiasis under Flood in Anhui Province

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Longxing Qi ◽  
Jing-an Cui ◽  
Tingting Huang ◽  
Fengli Ye ◽  
Longzhi Jiang
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Anhui Province ◽  
Endemic Equilibrium ◽  
Observation Data ◽  
Schistosomiasis Control ◽  
The Stability ◽  
The Impact ◽  
The Basic Reproduction Number

Based on the real observation data in Tongcheng city, this paper established a mathematical model of schistosomiasis transmission under flood in Anhui province. The delay of schistosomiasis outbreak under flood was considered. Analysis of this model shows that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. The stability of the unique endemic equilibrium may be changed under some conditions even if the basic reproduction number is larger than one. The impact of flood on the stability of the endemic equilibrium is studied and the results imply that flood can destabilize the system and periodic solutions can arise by Hopf bifurcation. Finally, numerical simulations are performed to support these mathematical results and the results are in accord with the observation data from Tongcheng Schistosomiasis Control Station.

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