Mathematical modelling of drug resistant malaria parasites and vector populations

Abstract

SUMMARYIn this paper, we describe the phenomenon of drug resistant malaria infection in a hyperendemic region by a system of ordinary di erential equations models. Di erent situations on both vectors and humans are described. The ÿrst presentations deal with single population each for both humans and vectors (with the human population ÿxed). These models are without resistant strains. The second group of models deal with both resistant and sensitive strains. Our focus in analysing the models is on establishing a unique positive asymptotic equilibrium for each of them. It is shown that (under suitable conditions in most cases) the equilibrium points are (locally) asymptotically stable. The biological signiÿcance of each of these points emerges as a by-product.

Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

“…and let m ¼ N V N H be the female vector-human ratio defined as the number of female sandflies per human host (see similar definition in malaria models, in [1,17]). Note that the ratio m is taken as a constant because it is well known (see [37] pages 218-220) that a vector takes a fixed number of blood-meals per unit time independent of the population density of the host.…”

“…main, and thus, the model is epidemiologically and mathematically well-posed, and it is sufficient to consider the dynamics of the flow generated by (1) in this positively-invariant domain X.…”

Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)

“…, in the classes S H , I H , R H , S V , and I V of the populations, respectively, and m is the female vector host ratio, defined as the number of female mosquitoes per human host [2,15,33]. This gives the following system of equations…”

Dynamics of an age-structured two-strain model for malaria transmission

“…In the absence of an effective and safe vaccine for use against malaria in humans (although concerted global efforts are underway to develop such a vaccine [5,15,16,24,31,[39][40][41]44,48,49,53,57,59]), malaria control is based on the use of preventive measures (such as mosquito-reduction strategies and personal protection against mosquito bite) and the use of anti-malaria drugs (see, for instance, [20,21,32,46,47,61,63]). The use of anti-malarial drugs (such as Aralen, Chloroquine, Malaraquine and Nivaquine [6,43]) is, however, known to pose the problem of the emergence and transmission of drug-resistant malaria strain [3,6,20,32,33,43]. Such resistance is attributed to factors such as [3,6,20,32,33,43]:…”