scholarly journals The Impact of Vaccination on Covid-19 Disease Transmission Patterns in a Human Population: A Theoretical Analysis

2021 ◽  
pp. 1-14
Author(s):  
A. B. Okrinya ◽  
C. N. Timinibife
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Human Population ◽  
Index Case ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Disease Eradication ◽  
Free Region ◽  
The Impact ◽  
Disease Free

We construct a Mathematical model that describes the effect of vaccination on the dynamics of the transmission of COVID-19 disease in a human population. The model is a system of ordinary differential equations that describes the evolution of humans in a range of Covid-19 states due to emergence of an index case in a disease free region. The analysis of the model shows that effective vaccination can lead to disease eradication, where in the disease free state is locally asymptomatically stable if the basic reproductive number, and unstable when The numerical simulations suggests the use of other social measures alongside  vaccination in order to avert the possibility of the disease  becoming endemic.

scholarly journals Mathematical modelling for malaria under resistance and population movement

2020 ◽  
Vol 38 (2) ◽  
pp. 133-163
Author(s):  
Cristhian Montoya ◽  
Jhoana P. Romero Leiton
Keyword(s):  
Human Population ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Transmission Dynamic ◽  
Equilibrium Solutions ◽  
Population Movements ◽  
Existence And Stability ◽  
Theoretical Results ◽  
Disease Free

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formulated. Numerical experiments are carried out in both models to show the feasibility of our theoretical results.

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.

Boundedness and Stability Properties of Solutions of Mathematical Model of Measles.

2021 ◽  
Vol 52 (1) ◽  
pp. 91-112
Author(s):  
Babatunde Sunday Ogundare ◽  
James Akingbade
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Jacobian Determinant ◽  
Stability Of Solutions ◽  
Open Population ◽  
Disease Free

In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.

scholarly journals Rich Dynamics of an Epidemic Model with Saturation Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Medical Resource ◽  
Sir Epidemic Model ◽  
The Impact ◽  
The Basic Reproduction Number

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

scholarly journals Pesticide application, educational treatment and infectious respiratory diseases: A mechanistic model with two impulsive controls

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243048
Author(s):  
Juan Pablo Gutiérrez-Jara ◽  
Fernando Córdova-Lepe ◽  
María Teresa Muñoz-Quezada ◽  
Gerardo Chowell
Keyword(s):  
Respiratory Disease ◽  
Disease Transmission ◽  
Pesticide Exposure ◽  
Transmission Rate ◽  
Toxic Substance ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Pesticide Use ◽  
Educational Treatment ◽  
The Impact

In this paper, we develop and analyze an SIS-type epidemiological-mathematical model of the interaction between pesticide use and infectious respiratory disease transmission for investigating the impact of pesticide intoxication on the spread of these types of diseases. We further investigate the role of educational treatment for appropriate pesticide use on the transmission dynamics. Two impulsive control events are proposed: pesticide use and educational treatment. From the proposed model, it was obtained that the rate of forgetfulness towards educational treatment is a determining factor for the reduction of intoxicated people, as well as for the reduction of costs associated with educational interventions. To get reduced intoxications, the population’s fraction to which is necessary to apply the educational treatment depends on its individual effectiveness level and the educational treatments’ forgetfulness rate. In addition, the turnover of agricultural workers plays a fundamental role in the dynamics of agrotoxic use, particularly in the application of educational treatment. For illustration, a flu-like disease with a basic reproductive number below the epidemic threshold of 1.0 is shown can acquire epidemic potential in a population at risk of pesticide exposure. Hence, our findings suggest that educational treatment targeting pesticide exposure is an effective tool to reduce the transmission rate of an infectious respiratory disease in a population exposed to the toxic substance.

scholarly journals Mathematical Modelling of the Dynamics of COVID-19 Disease Transmission

2021 ◽  
pp. 123-137
Author(s):  
A. B. Okrinya ◽  
E. Esekhaigbe
Keyword(s):  
Disease Transmission ◽  
Human Population ◽  
Reproduction Number ◽  
Index Case ◽  
Asymptotically Stable ◽  
Simple Mathematical Model ◽  
Oscillatory Behaviour ◽  
Disease Free ◽  
The Basic Reproduction Number

We construct a simple mathematical model that describes the dynamics of the transmission of COVID-19 disease in a human population. It accounts for the various phases of the disease and its mode of contact through infectious humans and surfaces. The contribution of asymptomatic humans in the dynamics of the disease is well represented. The model is a system of ordinary dierential equations that describes the evolution of humans in a range of COVID-19 states due to emergence of an index case. The analysis includes establishment of the basic reproduction number, R0, where, R0 < 1 signifies a disease free state that is locally asymptotically stable. A key result in this study shows some long term damped oscillatory behaviour that do not seem to end soon.

scholarly journals Modelling and Simulating a Transmission of COVID-19 Disease: Niger Republic Case

2020 ◽  
Vol 13 (3) ◽  
pp. 549-566
Author(s):  
Abba Mahamane Oumarou ◽  
Saley Bisso
Keyword(s):  
Matrix Method ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Impact ◽  
Disease Free

This paper focuses on the dynamics of spreads of a coronavirus disease (Covid-19).Through this paper, we study the impact of a contact rate in the transmission of the disease. We determine the basic reproductive number R0, by using the next generation matrix method. We also determine the Disease Free Equilibrium and Endemic Equilibrium points of our model. We prove that the Disease Free Equilibrium is asymptotically stable if R0 < 1 and unstable if R0 > 1. The asymptotical stability of Endemic Equilibrium is also establish. Numerical simulations are made to show the impact of contact rate in the spread of disease.

scholarly journals AN SEIR MODEL WITH INFECTIOUS LATENT AND A PERIODIC VACCINATION STRATEGY

2021 ◽  
Vol 26 (2) ◽  
pp. 236-252
Author(s):  
Islam A. Moneim
Keyword(s):  
Infectious Diseases ◽  
Periodic Solutions ◽  
Disease Transmission ◽  
Vaccination Strategy ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
New Wave ◽  
Globally Asymptotically Stable ◽  
Seir Model ◽  
The Impact

An SEIR epidemic model with a nonconstant vaccination strategy is studied. This SEIR model has two disease transmission rates β1 and β2 which imitate the fact that, for some infectious diseases, a latent person can pass the disease into a susceptible one. Here we study the spread of some childhood infectious diseases as good examples of diseases with infectious latent. We found that our SEIR model has a unique disease free solution (DFS). A lower bound and an upper bound of the basic reproductive number, R0 are estimated. We show that, the DFS is globally asymptotically stable when and unstable if Computer simulations have been conducted to show that non trivial periodic solutions are possible. Moreover the impact of the contact rate between the latent and the susceptibles is simulated. Different periodic solutions with different periods including one, two and three years, are obtained. These results give a clearer view for the decision makers to know how and when they should take action against a possible new wave of these infectious diseases. This action is mainly, applying a suitable dose of vaccination just before a severe peak of infection occurs.

scholarly journals A Schistosomiasis Model with Praziquantel Resistance

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Longxing Qi ◽  
Jing-an Cui
Keyword(s):  
Drug Treatment ◽  
Resistant Strain ◽  
Genetic Resistance ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Boundary Equilibrium ◽  
Existence And Stability ◽  
The Impact ◽  
Emergence Of Resistance ◽  
Disease Free

A compartmental model is established for schistosomiasis with praziquantel resistance. The model considers the impact of genetic resistance and drug treatment on the transmission of schistosomiasis. We calculate the basic reproductive number and discuss the existence and stability of disease-free equilibrium, boundary equilibrium, and coexistence equilibrium. Our analysis shows that regardless of whether drug treatment leads to the emergence of resistance, once the impact of genetic resistance is larger, the resistant strain will be dominant, which is detrimental to the control of schistosomiasis. In addition, once the proportion of human with drug-resistant strain produced by drug treatment is larger, the number of human and snails with resistant strain is larger. This is not a good result for drug treatment with praziquantel.

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.

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