A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria

Chiyaka, Christinah; Tchuenche, Jean M.; Garira, Winston; Dube, Simiso

doi:10.1016/j.amc.2007.05.016

Cited by 87 publications

(60 citation statements)

References 30 publications

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“…This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al (2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed. …”

supporting

confidence: 83%

“…Nowadays, though, malaria control depends mostly on personal protection, and treatment [15,16]. In this paper, we modify the mathematical model proposed by Chiyaka et al [15], for the effects of control strategies on malaria transmission, to become a non integer order model.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we modify the mathematical model proposed by Chiyaka et al [15], for the effects of control strategies on malaria transmission, to become a non integer order model. We aim to build a better approximation model to the real dynamics of malaria transmission among heterogeneous populations.…”

Section: Introductionmentioning

confidence: 99%

“…We consider the integer order model proposed by Chiyaka et al (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b.…”

mentioning

confidence: 99%

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Fractional model for malaria transmission under control strategies

Pinto

Machado

2013

Computers & Mathematics with Applications

103

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a b s t r a c tWe study a fractional model for malaria transmission under control strategies. We consider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al. (2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

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supporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Fractional model for malaria transmission under control strategies

Pinto

Machado

2013

Computers & Mathematics with Applications

103

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“…He showed that reducing the number of mosquitoes has little effect on the epidemiology of malaria in areas of intense transmission [2]. Nowadays, several mathematical models have been developed in order to reduce the malaria death rate in the world [3,4]. In spite of the efforts made, it is still difficult to predict future malaria intensity, particularly in view of climate change.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality

Traoré

Sangaré

Traoré

2017

Journal of Applied Mathematics

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In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.

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Dynamical and numerical analysis of the hepatitis B virus treatment model through fractal–fractional derivative

Al‐sadi,

Wei,

Abdullah

et al. 2024

Math Methods in App Sciences

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Infection with the hepatitis B virus (HBV) is a global health problem and may be controlled via appropriate treatment. We use fractional models to understand infectious diseases because fractional models help us understand treatments' effects on hepatitis B better than integer‐order models. In this article, we introduce a new mathematical model for HBV based on the fractal–fractional derivative with a generalized Mittag–Leffler kernel. Firstly, we discuss the fundamental properties, like the equilibria of the model and the primary reproduction number. Then, we investigate the existence of a unique solution to our model. We use an iterative method to solve the proposed model. Further, we discuss the stability of the model through stability theory. Finally, we offer some graphical illustrations for various values of the parameters.

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A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria

Cited by 87 publications

References 30 publications

Fractional model for malaria transmission under control strategies

Fractional model for malaria transmission under control strategies

A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality

Dynamical and numerical analysis of the hepatitis B virus treatment model through fractal–fractional derivative

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