Simple Mathematical Model for Malaria Transmission

Osman, Mojeeb AL-Rahman EL-Nor; Adu, Isaac Kwasi

doi:10.9734/jamcs/2017/37843

Cited by 21 publications

(10 citation statements)

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“…Since the earliest Ross model [37], several extensions have been made based on the use of autonomous [e.g. 1,9,18,19,29,33] and non-autonomous [e.g. 4,10,28,32] mathematical models to facilitate understanding of the dynamical spread of malaria between humans and mosquitoes interacting populations.…”

Section: Introductionmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equilibria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

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Section: Introductionmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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“…Reference [21] used a simple mathematical model to demonstrate the interrelationships between different interventions and the potential for malaria elimination when they are combined. Based on this, we formulate and analyze a malaria model as an SEIRS for the host population and SEI for the vector population similar to that of [17][18][19][20] e transition diagram for the proposed model is presented in Figure 1. Table 1 shows the parameters used in the model 1 and their interpretations.…”

Section: Proposed Model Of Malaria Transmissionmentioning

confidence: 99%

“…It has been shown that the transmission of malaria is highly influenced by the dynamics of immature mosquitoes. Reference [19] considered SEIR − SEI model of malaria transmission between humans and mosquitoes. ey concluded that malaria may be controlled by reducing the contact rate between human and mosquito, the use of active malaria drugs, insecticides, and mosquito treated nets can help to reduce mosquitoes' population and malaria transmission, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for Effective Control and Possible Eradication of Malaria

Adom-Konadu

Yankson

Naandam

et al. 2022

Journal of Mathematics

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In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies α and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α was found to be the most sensitive parameter in the reduction of ℛ 0 . Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40 % of adherence to the preventive strategies coupled with about 40 % of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.

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“…The next-generation matrix from the product of equation (17) calculated by FV −1 is obtained as Thus, the fundamental reproduction number R 0 = ρðF V −1 Þ where ρ is the dominant eigenvalue of the product F V −1 and the R 01 and R 02 at disease free equilibrium E 1 and E 2 are obtained, respectively, in equations ( 19) and (20) as given by…”

Section: Model Description and Formulationmentioning

confidence: 99%

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Keno

Dano

Makinde

2022

Computational and Mathematical Methods

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In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

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Simple Mathematical Model for Malaria Transmission

Cited by 21 publications

References 0 publications

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

A Mathematical Model for Effective Control and Possible Eradication of Malaria

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

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