Calistus N. Ngonghala

The impact of bed-net use on malaria prevalence

Malaria infection continues to be a major problem in many parts of the world including the Americas, Asia, and Africa. Insecticide-treated bed-nets have shown to reduce malaria cases by 50%; however, improper handling and human behavior can diminish their effectiveness. We formulate and analyze a mathematical model that considers the transmission dynamics of malaria infection in mosquito and human populations and investigate the impact of bed-nets on its control. The effective reproduction number is derived and existence of backward bifurcation is presented. The backward bifurcation implies that the reduction of R below unity alone is not enough to eradicate malaria, except when the initial cases of infection in both populations are small. Our analysis demonstrate that bed-net usage has a positive impact in reducing the reproduction number R. The results show that if 75% of the population were to use bed-nets, malaria could be eliminated. We conclude that more data on the impact of human and mosquito behavior on malaria spread is needed to develop more realistic models and better predictions.

Poverty, Disease, and the Ecology of Complex Systems

Coupled models of ecology and economic growth can provide key insights into the formation of poverty traps that arise from complex interactions between biosocial and biophysical processes.

Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission

A deterministic ordinary differential equation model for the dynamics of malaria transmission that explicitly integrates the demography and life style of the malaria vector and its interaction with the human population is developed and analyzed. The model is different from standard malaria transmission models in that the vectors involved in disease transmission are those that are questing for human blood. Model results indicate the existence of nontrivial disease free and endemic steady states, which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. Our model therefore captures oscillations that are known to exist in the dynamics of malaria transmission without recourse to external seasonal forcing. Additionally, our model exhibits the phenomenon of backward bifurcation. Two threshold parameters that can be used for purposes of control are identified and studied, and possible reasons why it has been difficult to eradicate malaria are advanced.

Quantifying the impact of decay in bed-net efficacy on malaria transmission

Insecticide-treated nets (ITNs) are at the forefront of malaria control programs and even though the percentage of households in sub-Saharan Africa that owned nets increased from 3% in 2000 to 53% in 2012, many children continue to die from malaria. The potential impact of ITNs on reducing malaria transmission is limited due to inconsistent or improper use, as well as physical decay in effectiveness. Most mathematical models for malaria transmission have assumed a fixed effectiveness rate for bed-nets, which can overestimate the impact of nets on malaria control. We develop a model for malaria spread that captures the decrease in ITN effectiveness due to physical and chemical decay, as well as human behavior as a function of time. We perform uncertainty and sensitivity analyses to identify and rank parameters that play a critical role in malaria transmission. These analyses show that the basic reproduction number R0, and the infectious human population are most sensitive to bed-net coverage and the biting rate of mosquitoes. Our results show the existence of a backward bifurcation for the case in which ITN efficacy is constant over time, which occurs for some range of parameters and is characterized by high malaria mortality in humans. This result implies that bringing R0 to less than one is not enough for malaria elimination but rather additional efforts will be necessary to control the disease. For the case in which ITN efficacy decays over time, we determine coverage levels required to control malaria for different ITN efficacies and demonstrate that ITNs with longer useful lifespans perform better in malaria control. We conclude that malaria control programs should focus on increasing bed-net coverage, which can be achieved by enhancing malaria education and increasing bed-net distribution in malaria endemic regions.

Persistent oscillations and backward bifurcation in a malaria model with varying human and mosquito populations: implications for control

We derive and study a deterministic compartmental model for malaria transmission with varying human and mosquito populations. Our model considers disease-related deaths, asymptomatic immune humans who are also infectious, as well as mosquito demography, reproduction and feeding habits. Analysis of the model reveals the existence of a backward bifurcation and persistent limit cycles whose period and size is determined by two threshold parameters: the vectorial basic reproduction number

Clusters of poverty and disease emerge from feedbacks on an epidemiological network.

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Environmental transmission of Mycobacterium ulcerans drives dynamics of Buruli ulcer in endemic regions of Cameroon

Rm, and the disease basic reproduction number