Global analysis of a mathematical model on malaria with competitive strains and immune responses

Chen, Hongyan; Wang, Wendi; Fu, Rui; Luo, Jianfeng

doi:10.1016/j.amc.2015.02.073

Cited by 15 publications

(12 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By similar discussions to those in [3], we get the nonnegativity of solutions of model (2.2), which is stated by the following lemma.…”

Section: Preliminary Analysis Of the Modelmentioning

confidence: 60%

Mathematical Analysis of an Obesity Model with Eating Behaviors

Wang¹

2020

CSIAM-AM

Self Cite

View full text Add to dashboard Cite

Overweight is a social disease, which is transmitted through social networks. A mathematical model is proposed to simulate the dynamics of social obesity, where the structures of individual heterogeneity and overeating behaviors are incorporated. The basic reproduction number of the disease is calculated and is shown to be a threshold for disease invasion. Sufficient conditions for the global stability of an endemic equilibrium is established by Lyapunov functions. Numerical simulations are provided to reveal how interventions through treatment to eating behaviors and eduction to susceptible individuals suppress the progression of the disease.

show abstract

“…By similar discussions to those in [3], we get the nonnegativity of solutions of model (2.2), which is stated by the following lemma.…”

Section: Preliminary Analysis Of the Modelmentioning

confidence: 60%

Mathematical Analysis of an Obesity Model with Eating Behaviors

Wang¹

2020

CSIAM-AM

Self Cite

View full text Add to dashboard Cite

show abstract

“…Plasmodium falciparum (P. falciparum) is the most popular malaria parasite and it is accounted for the highest number of malaria cases [1]. The other four Plasmodium species that infect humans are P. vivax, P. ovale, P. malariae and P. knowlesi [2,3]. The malaria infection within a host is composed of two phases, the liver stage and the blood stage [3].…”

Section: Introductionmentioning

confidence: 99%

“…The sporozoites migrate to the liver where they infect the liver cells and develop into schizonts. After rupturing, the schizonts release the parasites in the form of merozoites into the bloodstream where the blood stage starts [2,4,5]. The merozoites invade red blood cells and develop within them through three morphological stages.…”

Section: Introductionmentioning

confidence: 99%

“…They performed experiments to estimate the invasion rate of red blood cells. Tumwiine et al [26] explored an extended version of model (2), where they established the existence and global stability of equilibrium points. Niger and Gumel [4] extended the models in [20] and [22] by adding the effects of immune response and malaria vaccines.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, some works have differentiated between the immune response that targets infected red blood cells, and the immune response that targets free merozoites. For instance, Chen et al [2] studied a blood-stage malaria infection model with two competitive strains of P. falciparum and two types of immune responses, namely cellular immunity and antibody immunity. The infection rates and the stimulation rates of the immune responses are provided by saturated rates.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response

Ełaiw

Agha

2020

Mathematics

View full text Add to dashboard Cite

Malaria is one of the most dangerous global diseases. This paper studies a reaction-diffusion model for the within-host dynamics of malaria infection with both antibody and cell-mediated immune responses. The model explores the interactions between uninfected red blood cells (erythrocytes), three types of infected red blood cells, free merozoites, CTLs and antibodies. It contains some parameters to measure the effect of antimalarial drugs and isoleucine starvation on the blood cycle of malaria infection. The basic properties of the model are discussed. All possible equilibrium points and the threshold conditions required for their existence are addressed. The global stability of all equilibria are proved by selecting suitable Lyapunov functionals and using LaSalle’s invariance principle. The characteristic equations are used to study the local instability conditions of the equilibria. Some numerical simulations are conducted to support the theoretical results. The results indicate that antimalarial drugs with high efficacy can clear the infection and take the system towards the disease-free state. Increasing the efficacy of isoleucine starvation has a similar effect as antimalarial drugs and can eliminate the disease. The presence of immune responses with low efficacy of treatments does not provide a complete protection against the disease. However, the immune responses reduce the concentrations of all types of infected cells and limit the production of malaria parasites.

show abstract

A spectrally accurate time–space pseudospectral method for reaction–diffusion Malaria infection model

Mittal

2022

Comp. Appl. Math.

View full text Add to dashboard Cite

Global analysis of a mathematical model on malaria with competitive strains and immune responses

Cited by 15 publications

References 39 publications

Mathematical Analysis of an Obesity Model with Eating Behaviors

Mathematical Analysis of an Obesity Model with Eating Behaviors

Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response

A spectrally accurate time–space pseudospectral method for reaction–diffusion Malaria infection model

Contact Info

Product

Resources

About