The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission

Wedajo, Alemu Geleta

doi:10.11648/j.ajam.20180603.13

Cited by 6 publications

(9 citation statements)

References 12 publications

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“…the parameters d = P K usually called the carrying capacity [31]. Hence all feasible solutions set of the human population of the model (1) enters the region.…”

Section: Invariant Regionmentioning

confidence: 99%

Modelling and Analysis of Effect of Awareness Programs by Media on the Spread of COVID-19 Pandemic Disease

Kobe¹

2020

MCS

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This paper proposes and analyses a basic deterministic mathematical model to investigate Modeling and Analysis of effect of awareness program by media on the spread COVID-19 Pandemic Disease. The model has seven non-linear differential equations, which describe the effects of awareness programs by media on the spread of COVID-19 Pandemic diseases. Analytical study carried out to investigate the model analysis and existence of stability of system, given threshold parameters known as the basic reproduction number, which obtained using next generation matrix method. The equilibrium of COVID 19 models is determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the basic reproduction number less than one, COVID 19 model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The analysis and simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of COVID 19 pandemic were suggest using that awareness programs through the media campaigning are helpful in decreasing the spread of COVID 19 Pandemic diseases by isolating a fraction of susceptible from infective.

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“…the parameters d = P K usually called the carrying capacity [31]. Hence all feasible solutions set of the human population of the model (1) enters the region.…”

Section: Invariant Regionmentioning

confidence: 99%

Modelling and Analysis of Effect of Awareness Programs by Media on the Spread of COVID-19 Pandemic Disease

Kobe¹

2020

MCS

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“…Using the interactions illustrated by Figure 1, the dynamics of the transmission given by the system of non linear differential equations (1).…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…In this subsection we provide further simulations showing the varying effects of the immunity parameters (µ, λ, σ and θ) on the behaviour of the system (1). We analyze these effects for R 0 > 1.…”

Section: The Varying Effects Of the Immunity Parameters On The Behavimentioning

confidence: 99%

Mathematical Analysis of an Immune-structured Chikungunya Transmission Model

Famane¹,

Elisée

Sadou

et al. 2019

Eur. J. Pure Appl. Math.

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In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

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“…It is already shown that the DFE of model ( 1) -( 4) is given bf e = 9 ⁄ , 0, 0, 0A. Now, following [5][6][7][8] the stability analysis of DFE is conducted and the results are presented in the form of theorems and proofs in the following.…”

Section: Stability Analysis Of the Disease Free Equilibriummentioning

confidence: 99%

Modeling and Analysis of Population Dynamics of Human Cells Pertaining to HIV/AIDS with Treatment

Regassa¹,

Koya²

2019

AJAM

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In this paper, a mathematical model has been formulated to describe the population dynamics of human cells pertaining to the HIV/AIDS disease with ART as treatment and is analyzed. The human cells have been divided into four compartments Susceptible -Asymptomatic -Symptomatic -AIDS (SAIV). The well posedness of the four dimensional dynamical system is proved and the steady states of the model are identified. Additionally, parametric expression for the basic reproduction number is constructed following next generation matrix method and analyzed its stability using Routh Hurwitz criterion. From the analytical and numerical simulation studies it is observed that if the basic reproduction is less than one unit then the solution converges to the disease free steady state i.e., disease will wipe out and thus the treatment is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the treatment is said to be unsuccessful. Sensitivity analysis of the model parameters is conducted and their impact on the reproduction number is analyzed. Finally, the model of the present study simulated using MATLAB. The results and observations have been included in the text of this paper lucidly.

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The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission

Cited by 6 publications

References 12 publications

Modelling and Analysis of Effect of Awareness Programs by Media on the Spread of COVID-19 Pandemic Disease

Modelling and Analysis of Effect of Awareness Programs by Media on the Spread of COVID-19 Pandemic Disease

Mathematical Analysis of an Immune-structured Chikungunya Transmission Model

Modeling and Analysis of Population Dynamics of Human Cells Pertaining to HIV/AIDS with Treatment

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