Structured deterministic models applied to malaria and other endemic diseases

This thesis includes modeling studies on three structured deterministic models. These models are used to study the disease dynamics of malaria or the joint disease dynamics of HIV and HSV-2. Each of the models includes multiple components containing individuals in various epidemiological classes for the purpose of addressing questions that are of interests to biologists and epidemiologists. Some of the compartments have a continuous age-structure, which is necessary for studying the specific biological questions under investigation.^ In Chapter 2 a chronological-age structured deterministic model for malaria is presented. The model includes the human and mosquito populations with the human population structured by chronological age. The model consists of both PDEs and ODEs. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original PDE model is reduced to an ODE model with aging. The basic reproduction number R0 is derived for both settings of the model. A novel assumption of the model based on biological evidence is that the infectiousness of chronic infected individuals can be triggered by bites from even susceptible mosquitoes. The model analysis indicates that this assumption contributes greatly to the R0 and therefore needs to be further studied and understood. Numerical simulations for n =2 age groups and a sensitivity/uncertainty analysis show that it is important to both asymptomatic infectious individuals and asymptomatic chronic infections. Age-targeted control strategies are also discussed.^ In Chapter 3 a deterministic malaria model is presented to study the effects of a pre-erythrocytic vaccine on malaria dynamics. The model includes two vaccinated classes, the first for initial vaccination dose(s) and the second for a booster dose. Vaccinated individuals in both compartments are structured by vaccine-age. A vaccine-age dependent transition between vaccinated classes makes it possible to model a minimum vaccine-age required for receiving the booster vaccination. The control reproduction number R is derived and shown to determine the local stability of the disease free equilibrium. Global stability of the disease free equilibrium is shown analytically under certain assumptions and conditions for the existence of endemic equilibria are identified. Numerical results suggest that the incorporation of two vaccination classes, as opposed to only one, allows for a greater accuracy in predicting threshold vaccination coverages for disease eradication. The model also exhibits backward bifurcation, indicating thatR=1 is no longer the threshold value for disease eradication. The effect of waning vaccine efficacy (vaccine-age dependent) on disease prevalence is also investigated. ^ Chapter 4 presents a deterministic model for the joint dynamics of HIV and HSV-2 to study the effect that the presence of HSV-2 may have on the prevalence of HIV. An infection-age is used to incorporate the epidemiological characteristic of HSV-2 that infected individuals change between the acute and the latent stages, and treatment may affect the lengths of these stages. The model is also structured by gender and includes one male and two female populations with different activity levels. The basic reproduction number for each disease, as well as the invasion reproduction numbers are derived. Due to the model complexity, the derivation of these reproduction numbers and their biological interpretations are very challenging, which is one of the novel aspects of this study. Numerical simulations are performed to confirm and extend the analytical results. A sensitivity analysis is also conducted. Model results demonstrate that strategies for reducing co-infections with HIV and HSV-2, particularly treating the high-risk group of females may have an important impact on the HIV disease dynamics

Models for measuring and predicting malaria vaccine efficacy

In the past decade several candidate malaria vaccines have undergone clinical trials in artificial challenge studies and studies of natural infection under field conditions. GlaxoSmithKline’s RTS,S vaccine against Plasmodium falciparum infection has taken the lead, with Phase III trials in African children demonstrating 55.8% (97.5% CI, 51.3% - 59.8%) efficacy against clinical malaria and 34.8% (95% CI, 16.2% – 49.2%) efficacy against severe malaria. Mathematical models can contribute to multiple stages of malaria vaccine development, from measuring efficacy in clinical trials, understanding the relationship between naturally acquired and vaccine-induced immunity, identifying correlates of protection, and predicting the likely impact of vaccination programs in the field. When measuring vaccine efficacy in field trials under natural exposure to malaria, there are many factors which can bias estimates of efficacy. We demonstrate how heterogeneity in exposure can cause efficacy to be underestimated and heterogeneity in vaccine response can cause efficacy to be overestimated. Most infection-blocking vaccines rely on boosting some element of the pre-erythrocytic immune response, however the relationship between the naturally acquired pre-erythrocytic responses and protection from infection remains poorly understood. By analysing studies from a systematic of the published literature, I demonstrate that although many studies report a statistically significant relationship between cellular pre-erythrocytic immune responses and protection from infection, many studies do not have sufficient statistical power to evaluate the effects of the pre-erythrocytic immune response. Mathematical models are developed for investigating the relationship between pre-erythrocytic antibodies and protection from infection, and fitted to data from a longitudinal study of malaria infection in Kenyan adults. The relationship between antibodies to the antigens circumsporozoite protein (CSP) and thrombospondin-related adhesion protein (TRAP) and protection from infection is characterised using dose-response curves. Using data from an artificial challenge trial of the RTS,S malaria vaccine, I demonstrate that vaccine-induced protection from infection depends on both anti-CSP antibodies and CSP-specific T cells. I estimate that RTS,S causes a 97.7% (95% CI, 96.3% – 98/7%) reduction in the number of parasites entering the blood from the liver. The immune effector mechanisms determining the duration of vaccine-induced protection from infection are likely to be similar to those involved in naturally acquired immunity. Models of antibody kinetics were fitted to data from longitudinal studies of the antibody response to P. falciparum infection in Ghanaian and Gambian children, and the parameters determining the duration of antibody response are estimated. Upon licensure, a successful malaria vaccine is likely to be administered to young African children. A model of malaria transmission, extensively fitted to clinical data, is used to investigate the impact of vaccination in different transmission settings; the interaction between vaccines and other interventions such as insecticide treated nets; and the interaction between vaccination and naturally acquired immunity. Finally, the potential cost-effectiveness of vaccination is explored

Optimal Control For Malaria Epidemic Model With Vaccinating, Human Treatment And Mosquitos Spraying

In this paper we study the effect of vaccination control, medical treatment and spraying to malaria epidemic model.Firstly the non-control malaria epidemic model is generated and the equilibrium point is determined. Afterward, the stability of equilibrium point in previous model is investigated. The research is continued by deciding the optimal control of malaria epidemic model and minimizing the cost. The results show that the control effect can reduce the subpopulation of infected human and mosquitoes.In this paper we study the effect of vaccination control, medical treatment and spraying to malaria epidemic model.Firstly the non-control malaria epidemic model is generated and the equilibrium point is determined. Afterward, the stability of equilibrium point in previous model is investigated. The research is continued by deciding the optimal control of malaria epidemic model and minimizing the cost. The results show that the control effect can reduce the subpopulation of infected human and mosquitoes

Mathematical Modelling of Transmission Dynamics of Anthrax in Human and Animal Population.

Anthrax is an infectious disease that can be categorised under zoonotic diseases. It is caused by the bacteria known as Bacillus anthraces. Anthrax is one of the most leading causes of deaths in domestic and wild animals. In this paper, we develop and investigated a mathematical model for the transmission dynamics of the disease. Ordinary differential equations were formulated from the mathematical model. We performed the quantitative and qualitative analysis of the model to explain the transmission dynamics of the anthrax disease. We analysed and determined the model’s steady states solutions. The disease-free equilibrium of the anthrax model is analysed for locally asymptotic stability and the associated epidemic basic reproduction number. The model’s disease free equilibrium has shown to be locally asymptotically stable when the basic reproductive number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Sensitivity analysis was performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the diseases. Keywords: Anthrax model, Basic reproductive number, Asymptotic stability, Endemic equilibrium, Sensitivity analysis

Reducing Plasmodium falciparum malaria transmission in Africa: a model-based evaluation of intervention strategies.

BACKGROUND: Over the past decade malaria intervention coverage has been scaled up across Africa. However, it remains unclear what overall reduction in transmission is achievable using currently available tools. METHODS AND FINDINGS: We developed an individual-based simulation model for Plasmodium falciparum transmission in an African context incorporating the three major vector species (Anopheles gambiae s.s., An. arabiensis, and An. funestus) with parameters obtained by fitting to parasite prevalence data from 34 transmission settings across Africa. We incorporated the effect of the switch to artemisinin-combination therapy (ACT) and increasing coverage of long-lasting insecticide treated nets (LLINs) from the year 2000 onwards. We then explored the impact on transmission of continued roll-out of LLINs, additional rounds of indoor residual spraying (IRS), mass screening and treatment (MSAT), and a future RTS,S/AS01 vaccine in six representative settings with varying transmission intensity (as summarized by the annual entomological inoculation rate, EIR: 1 setting with low, 3 with moderate, and 2 with high EIRs), vector-species combinations, and patterns of seasonality. In all settings we considered a realistic target of 80% coverage of interventions. In the low-transmission setting (EIR approximately 3 ibppy [infectious bites per person per year]), LLINs have the potential to reduce malaria transmission to low levels (90%) or novel tools and/or substantial social improvements will be required, although considerable reductions in prevalence can be achieved with existing tools and realistic coverage levels. CONCLUSIONS: Interventions using current tools can result in major reductions in P. falciparum malaria transmission and the associated disease burden in Africa. Reduction to the 1% parasite prevalence threshold is possible in low- to moderate-transmission settings when vectors are primarily endophilic (indoor-resting), provided a comprehensive and sustained intervention program is achieved through roll-out of interventions. In high-transmission settings and those in which vectors are mainly exophilic (outdoor-resting), additional new tools that target exophagic (outdoor-biting), exophilic, and partly zoophagic mosquitoes will be required

Enteropathogen antibody dynamics and force of infection among children in low-resource settings.

Little is known about enteropathogen seroepidemiology among children in low-resource settings. We measured serological IgG responses to eight enteropathogens (Giardia intestinalis, Cryptosporidium parvum, Entamoeba histolytica, Salmonella enterica, enterotoxigenic Escherichia coli, Vibrio cholerae, Campylobacter jejuni, norovirus) in cohorts from Haiti, Kenya, and Tanzania. We studied antibody dynamics and force of infection across pathogens and cohorts. Enteropathogens shared common seroepidemiologic features that enabled between-pathogen comparisons of transmission. Overall, exposure was intense: for most pathogens the window of primary infection was <3 years old; for highest transmission pathogens primary infection occurred within the first year. Longitudinal profiles demonstrated significant IgG boosting and waning above seropositivity cutoffs, underscoring the value of longitudinal designs to estimate force of infection. Seroprevalence and force of infection were rank-preserving across pathogens, illustrating the measures provide similar information about transmission heterogeneity. Our findings suggest antibody response can be used to measure population-level transmission of diverse enteropathogens in serologic surveillance

Modeling infectious disease dynamics in the complex landscape of global health.

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health

Statistical methodology for the evaluation of vaccine efficacy in a phase III multi-centre trial of the RTS,S/AS01 malaria vaccine in African children

BACKGROUND\ud \ud There has been much debate about the appropriate statistical methodology for the evaluation of malaria field studies and the challenges in interpreting data arising from these trials.\ud \ud METHODS\ud \ud The present paper describes, for a pivotal phase III efficacy of the RTS, S/AS01 malaria vaccine, the methods of the statistical analysis and the rationale for their selection. The methods used to estimate efficacy of the primary course of vaccination, and of a booster dose, in preventing clinical episodes of uncomplicated and severe malaria, and to determine the duration of protection, are described. The interpretation of various measures of efficacy in terms of the potential public health impact of the vaccine is discussed.\ud \ud CONCLUSIONS\ud \ud The methodology selected to analyse the clinical trial must be scientifically sound, acceptable to regulatory authorities and meaningful to those responsible for malaria control and public health policy