Miranda I. Teboh-Ewungkem

Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamics

A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ0), is less than unity. Further, it has a unique endemic equilibrium if ℛ0>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛvac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine if ℛvac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level of gametocyte is critically important to the malaria burden in the community.

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.

Mathematical assessment of the effect of traditional beliefs and customs on the transmission dynamics of the 2014 Ebola outbreaks

BackgroundEbola is one of the most virulent human viral diseases, with a case fatality ratio between 25% to 90%. The 2014 West African outbreaks are the largest and worst in history. There is no specific treatment or effective/safe vaccine against the disease. Hence, control efforts are restricted to basic public health preventive (non-pharmaceutical) measures. Such efforts are undermined by traditional/cultural belief systems and customs, characterized by general mistrust and skepticism against government efforts to combat the disease. This study assesses the roles of traditional customs and public healthcare systems on the disease spread.MethodsA mathematical model is designed and used to assess population-level impact of basic non-pharmaceutical control measures on the 2014 Ebola outbreaks. The model incorporates the effects of traditional belief systems and customs, along with disease transmission within health-care settings and by Ebola-deceased individuals. A sensitivity analysis is performed to determine model parameters that most affect disease transmission. The model is parameterized using data from Guinea, one of the three Ebola-stricken countries. Numerical simulations are performed and the parameters that drive disease transmission, with or without basic public health control measures, determined. Three effectiveness levels of such basic measures are considered.ResultsThe distribution of the basic reproduction number (R0

A within-vector mathematical model of Plasmodium falciparum and implications of incomplete fertilization on optimal gametocyte sex ratio

\mathcal {R}_{0}

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

) for Guinea (in the absence of basic control measures) is such that R0∈[0.77,1.35]

Models and Proposals for Malaria: A Review

\mathcal {R}_{0}\in \;[0.77,1.35]

Male fecundity and optimal gametocyte sex ratios for Plasmodium falciparum during incomplete fertilization

, for the case when the belief systems do not result in more unreported Ebola cases. When such systems inhibit control efforts, the distribution increases to R0∈[1.15,2.05]

A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration

\mathcal {R}_{0}\in \;[1.15,2.05]

The effect of intermittent preventive treatment on anti-malarial drug resistance spread in areas with population movement

. The total Ebola cases are contributed by Ebola-deceased individuals (22%), symptomatic individuals in the early (33%) and latter (45%) infection stages. A significant reduction of new Ebola cases can be achieved by increasing health-care workers’ daily shifts from 8 to 24 hours, limiting hospital visitation to 1 hour and educating the populace to abandon detrimental traditional/cultural belief systems.ConclusionsThe 2014 outbreaks are controllable using a moderately-effective basic public health intervention strategy alone. A much higher (>50%) disease burden would have been recorded in the absence of such intervention. 2000 Mathematics Subject Classifications 92B05, 93A30, 93C15.

On a Reproductive Stage-Structured Model for the Population Dynamics of the Malaria Vector

A mathematical model that simulates the within-vector dynamics of Plasmodium falciparum in an Anopheles mosquito is developed, based on experimental data. The model takes a mosquitos blood meal as input and computes the salivary gland sporozoite load as the final output, a probable measure of mosquito infectivity. Computational model results are consistent with observed results in nature. Sensitivity analysis of the model parameters suggests that reducing the gametocyte density in the blood meal most significantly lowers sporozoite load in the salivary glands and hence mosquito infectivity, and is thus an attractive target for malaria control. The model is used to investigate the implication of incomplete fertilization on optimal gametocyte sex ratio. For a single strain, the transition from complete fertilization to increasingly incomplete fertilization shifts that ratio from 1 to N, where N is the number of viable male gametes produced by a single male gametocyte, towards 1 to 1, which is demonstrated to be the limiting ratio analytically. This ratio is then shown to be an evolutionarily stable strategy as well in the limiting case.