Habitat fragmentation promotes malaria persistence (original) (raw)

Mathematical models developed for studying malaria dynamics often focus on a single, homogeneous population. However, human movement connects environments with potentially different malaria transmission characteristics. To address the role of human movement and spatial heterogeneity in malaria transmission and malaria control, we consider a simple malaria metapopulation model incorporating two regions, or patches, connected by human movement, with different degrees of malaria transmission in each patch. Using our two-patch model, we calculate and analyzethe basic reproductionnumber, R0, anepidemiologicallyimportantthreshold quantity that indicates whether malaria will persist or go extinct in a population. Although R0 depends on the rates of human movement, we show that R0 is always bounded between the two quantities R01 and R02- the reproduction numbers for the two patches if isolated. If without migration, the disease is endemic in one patch but not in the other, then the addition...

In this article we consider a mathematical model of malaria transmission. We investigate both a reduced model which corresponds to the situation when the infected mosquito population equilibrates much faster than the human population and the full model. We prove that when the basic reproduction number is less than one, the disease-free equilibrium is the only equilibrium and it is locally asymptotically stable and if the reproduction number is greater than one, the disease-free equilibrium becomes unstable and an endemic equilibrium emerges and it is asymptotically stable. We also prove that, when the reproduction number is greater than one, there is a minimum wave speed c∗ such that a traveling wave solution exists only if the wave speed c satisfies c ≥ c∗. Finally, we investigate the relationship between spreading speed and diffusion coefficients. Our results show that the movements of mosquito population and human population will speed up the spread of the disease.

The present paper explores a simple dynamic model from which we review the classic formulae in malaria epidemiology that relate entomological and epidemiological variables to malaria transmission. In addition, we document the dynamics of malaria, illustrating the impact of control strategies and how the bites per mosquito have a larger effect on transmission intensity than the mosquito mortality, the ratio of mosquitoes to humans, or the transmission efficiency. The model has been built following the System Dynamics methodology, explicitly representing the variables, the feedbacks and the nonlinearities, i.e. the structure that governs the dynamics of the disease. In this sense, the paper offers a new way to obtain the most representative malaria indicators derived from stock-and-flow diagrams that encompass the causal relationships that exist between the attributes of such a system. Based on the obtained formulae from the human and mosquito sectors, we are able to eliminate three degrees of freedom, allowing us to calculate the temporal steady state relationship between Plasmodium falciparum prevalence in humans and mosquitoes. The model is generic in nature and may be parameterized to portray a wide variety of locations, different malaria parasites, vector species, and to cater for seasonality. Given that the model includes the principle mechanisms of malaria transmission, it acts as a foundation for simulations that represent the dynamics between humans and mosquitoes. Such model has been developed based on a number of simplifying assumptions. To the extent possible, the validity of the model under these assumptions has been analyzed by way of mathematic equations.

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.

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formul...