Mathematical modelling of malaria transmission and pathogenesis

In this thesis we will consider two mathematical models on malaria transmission and patho- genesis. The transmission model is a human-mosquito interaction model that describes the development of malaria in a human population. It accounts for the various phases of the disease in humans and mosquitoes, together with treatment of both sick and partially im- mune humans. The partially immune humans (termed asymptomatic) have recovered from the worst of the symptoms, but can still transmit the disease. We will present a mathematical model consisting of a system of ordinary differential equations that describes the evolution of humans and mosquitoes in a range of malarial states. A new feature, in what turns out to be a key class, is the consideration of reinfected asymptomatic humans. The analysis will include establishment of the basic reproduction number, R0, and asymptotic analysis to draw out the major timescale of events in the process of malaria becoming non-endemic to endemic in a region following introduction of a few infected mosquitoes. We will study the model to ascertain possible time scale in which intervention programmes may yield better results. We will also show through our analysis of the model some evidence of disease control and possible eradication. The model on malaria pathogenesis describes the evolution of the disease in the human host. We model the effect of immune response on the interaction between malaria parasites and erythrocytes with a system of delay differential equations in which there is time lag between the advent of malaria merozoites in the blood and the training of adaptive immune cells. We will study the model to ascertain whether or not a single successful bite of an infected mosquito would result in death in the absence of innate and adaptive immune response. Stability analysis will be carried out on the parasite free state in both the immune and non immune cases. We will also do numerical simulations on the model to track the development of adaptive immunity and use asymptotic methods, assuming a small delay to study the evolution of the disease in a naive individual following the injection of small amount of merozoites into the blood stream. The effect of different levels of innate immune response to the pathogenesis of the disease will be considered in the simulations to elicit a possible immune level that can serve as a guide to producing a vaccine with high efficacy level

Ecological immunology of mosquito-malaria interactions: Of non-natural versus natural model systems and their inferences

There has been a recent shift in the literature on mosquito/Plasmodium interactions with an increasingly large number of theoretical and experimental studies focusing on their population biology and evolutionary processes. Ecological immunology of mosquito-malaria interactions - the study of the mechanisms and function of mosquito immune responses to Plasmodium in their ecological and evolutionary context - is particularly important for our understanding of malaria transmission and how to control it. Indeed, describing the processes that create and maintain variation in mosquito immune responses and parasite virulence in natural populations may be as important to this endeavor as describing the immune responses themselves. For historical reasons, Ecological Immunology still largely relies on studies based on non-natural model systems. There are many reasons why current research should favour studies conducted closer to the field and more realistic experimental systems whenever possible. As a result, a number of researchers have raised concerns over the use of artificial host-parasite associations to generate inferences about population-level processes. Here I discuss and review several lines of evidence that, I believe, best illustrate and summarize the limitations of inferences generated using non-natural model systems

Placental Malaria and Mother-to-Child Transmission of Human Immunodeficiency Virus-1 in Rural Rwanda

We conducted a nested case-control study of placental malaria (PM) and mother-to-child transmission (MTCT) of human immunodeficiency virus-1 (HIV-1) within a prospective cohort of 627 mother-infant pairs followed from October 1989 until April 1994 in rural Rwanda. Sixty stored placentas were examined for PM and other placental pathology, comparing 20 HIV-infected mother-infant (perinatal transmitter) pairs, 20 HIV-uninfected pairs, and 20 HIV-infected mothers who did not transmit to their infant perinatally. Of 60 placentas examined, 45% showed evidence of PM. Placental malaria was associated with increased risk of MTCT of HIV-1 (adjusted odds ratio [aOR] = 6.3; 95% confidence interval [CI] = 1.4–29.1), especially among primigravidae (aOR = 12.0; 95% CI = 1.0–150; P < 0.05). Before antiretroviral therapy or prophylaxis, PM was associated with early infant HIV infection among rural Rwandan women living in a hyper-endemic malaria region. Primigravidae, among whom malaria tends to be most severe, may be at higher risk

Quantificando os efeitos do aquecimento global e das condições socioeconômicas locais na transmissão de malária

OBJETIVO: Apresenta-se um modelo matemático mostrando como esse instrumento pode ser importante para descrever a transmissão de malária. MÉTODOS: Baseado no modelo proposto previamente, foram quantificados os efeitos de dois fatores que podem afetar a transmissão da malaria: a temperatura ambiente e as condições socioeconômicas locais. RESULTADOS/CONCLUSÕES: A quantificação foi feita estudando o modelo proposto no estado estacionário e na sua dinâmica. Dependendo do nível de risco de malária, os principais efeitos na transmissão de malária são devidos à temperatura ambiente ou às condições socioeconômicas.OBJECTIVE: To show how a mathematical model can be used to describe and to understand the malaria transmission. METHODS: The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. RESULTS/CONCLUSIONS: The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions

Assessing The Effects Of Global Warming And Local Social And Economic Conditions On The Malaria Transmission.

To show how a mathematical model can be used to describe and to understand the malaria transmission. The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions.34214-2

Modelo de transmissão de malária em diferentes níveis de imunidade e de parâmetros temperatura-dependentes (vetor)

OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.OBJETIVO: Propõe-se um modelo compartimental para descrever a transmissão de malária, levando em consideração duas populações envolvidas: o hospedeiro humano e o vetor mosquito. MÉTODOS: Desenvolveu-se um modelo matemático baseado nas seguintes características: em relação ao hospedeiro humano, assumiu-se a existência de imunidade adquirida e de memória imunológica que, em uma reinfecção, leva ao reforço da resposta imune; em relação ao vetor mosquito, levou-se em consideração que o período médio de desenvolvimento desde ovo até mosquito adulto e o período de incubação extrínseco de parasitas (transformação de mosquitos infectados mas não-infecciosos em mosquitos infecciosos) são dependentes de temperatura ambiente. RESULTADOS: Foram obtidos os valores do equilíbrio no estado estacionário do modelo proposto. Da análise da estabilidade dos pontos de equilíbrio, foi determinada a razão de reprodutibilidade basal. CONCLUSÕES: Foi obtida uma variável epidemiológica importante, a razão de reprodutibilidade basal, que foi analisada em função dos parâmetros do modelo

A Mathematical Model For Malaria Transmission Relating Global Warming And Local Socioeconomic Conditions.

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.35322423

Malaria Transmission Model For Different Levels Of Acquired Immunity And Temperature-dependent Parameters (vector).

Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.34223-3