A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host

Sangaré

Journal of Biological Dynamics

2018

In this paper, we present a mathematical model of malaria transmission dynamics with age structure for the vector population and a periodic biting rate of female anopheles mosquitoes. The human population is divided into two major categories: the most vulnerable called non-immune and the least vulnerable called semi-immune. By applying the theory of uniform persistence and the Floquet theory with comparison principle, we analyse the stability of the diseasefree equilibrium and the behaviour of the model when the basic reproduction ratio R 0 is greater than one or less than one. At last, numerical simulations are carried out to illustrate our mathematical results. ARTICLE HISTORY

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A mathematical model of malaria transmission in a periodic environment

Sangaré

Journal of Biological Dynamics

2018

“…Some have designed models to show how temperature alone influences malaria transmission [31], while others have focused on the theoretical effect of bed nets [32], multiple interventions [33] or climate change [34-36]. There is also a growing number of models that address the dynamics of immunity within individuals [37] and in communities [21,38]. …”

Section: Introductionmentioning

confidence: 99%

A dynamic model of some malaria-transmitting anopheline mosquitoes of the Afrotropical region. I. Model description and sensitivity analysis

Lunde

Korecha

Loha

et al. 2013

Malar J

BackgroundMost of the current biophysical models designed to address the large-scale distribution of malaria assume that transmission of the disease is independent of the vector involved. Another common assumption in these type of model is that the mortality rate of mosquitoes is constant over their life span and that their dispersion is negligible. Mosquito models are important in the prediction of malaria and hence there is a need for a realistic representation of the vectors involved.ResultsWe construct a biophysical model including two competing species, Anopheles gambiae s.s. and Anopheles arabiensis. Sensitivity analysis highlight the importance of relative humidity and mosquito size, the initial conditions and dispersion, and a rarely used parameter, the probability of finding blood. We also show that the assumption of exponential mortality of adult mosquitoes does not match the observed data, and suggest that an age dimension can overcome this problem.ConclusionsThis study highlights some of the assumptions commonly used when constructing mosquito-malaria models and presents a realistic model of An. gambiae s.s. and An. arabiensis and their interaction. This new mosquito model, OMaWa, can improve our understanding of the dynamics of these vectors, which in turn can be used to understand the dynamics of malaria.

“…Abu-Raddad et al (2006) and Mukandavire et al (2009) studied the influence of the interaction between HIV and malaria in a community. Differences in susceptibility, exposedness and infectivity between non-immune and semi-immune human hosts for malaria transmission were investigated by Ducrot et al (2009). Chamchod and Britton (2011) introduced a vector-bias model with vital dynamics to account for the greater attractiveness of infectious humans to mosquitoes.…”

mentioning

confidence: 99%

Mathematical Analysis of the Ross–Macdonald Model with Quarantine

Jin

Gao

2020

Bull Math Biol

People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors' advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number R 0 is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at R 0 = 1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as R 0 ≤ 1 and the unique endemic equilibrium is locally asymptotically stable as R 0 > 1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.