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Deterministic compartmental models form the simplest models in the mathematical study of infectious disease dynamics. They assume that a population is homogenous (all people are the same) and the only distinction is in their disease state.

Background As vaccination coverage against SARS-CoV-2 increases amidst the emergence and spread of more infectious and potentially more deadly viral variants, decisions on timing and extent of relaxing effective, but unsustainable, non-pharmaceutical interventions (NPIs) need to be made. Methods An individual-based transmission model of SARS-CoV-2 dynamics, OpenCOVID, was developed to compare the impact of various vaccination and NPI strategies on the COVID-19 epidemic in Switzerland. OpenCOVID uses the Oxford Containment Health Index (OCHI) to quantify the stringency of NPIs. Results Even if NPIs in place in March 2021 were to be maintained and the vaccine campaign rollout rapidly scaled-up, a ‘third wave’ was predicted. However, we find a cautious phased relaxation can substantially reduce population-level morbidity and mortality. We find that faster vaccination campaign can offset the size of such a wave, allowing more flexibility for NPI to be relaxed sooner. Model outcomes were most sensitive to the level of infectiousness of variants of concern observed in Switzerland. Conclusion A rapid vaccination rollout can allow the sooner relaxation of NPIs, however ongoing surveillance of - and swift responses to - emerging viral variants is of utmost importance for epidemic control., Graphical Abstract ga1

Additional file 1. Includes additional methods, figures, and tables that complement the analysis and results presented in the main manuscript.

Introduction Plus de 60 % des maladies infectieuses humaines sont imputables à des agents pathogènes communs avec les animaux (Karesh et al., 2012). Bien qu’un vaste corpus de connaissances existe sur la transmission intraspécifique des maladies infectieuses, nous en savons étonnamment peu sur la dynamique de transmission d’agents pathogènes zoonotiques entre espèces (Lloyd-Smith et al., 2009). Toutefois, pour comprendre...

One Health, « Une seule santé », est une stratégie mondiale visant à développer les collaborations interdisciplinaires pour la santé humaine, animale et environnementale. Elle promeut une approche intégrée, systémique et unifiée de la santé aux échelles locale, nationale et mondiale, afin de mieux affronter les maladies émergentes à risque pandémique, mais aussi s'adapter aux impacts environnementaux présents et futurs. Bien que ce mouvement s’étende, la littérature en français reste rare. Traduit de l’anglais, coordonné par d’éminents épidémiologistes et s'appuyant sur un large panel d' approches scientifiques rarement réunies autour de la santé, cet ouvrage retrace les origines du concept et présente un contenu pratique sur les outils méthodologiques, la collecte de données, les techniques de surveillance et les plans d’étude. Il combine recherche et pratique en un seul volume et constitue un ouvrage de référence unique pour la santé mondiale.

Additional file 1: A simple periodically forced difference equation model for mosquito population dynamics.

Additional file 8: S7. The Stan code for the delayed mortality model for both the intervention and the control arm in order to estimate the killing effect after biting.

Additional file 1. Supplementary data description and analysis.

Additional file 8: S7. The Stan code for the delayed mortality model for both the intervention and the control arm in order to estimate the killing effect after biting.

Additional file 3: Flowchart from operational to effective larviciding coverage.

Additional file 4: Re-simulated larviciding study in Mbita, western Kenya between 2002 and 2006.

We introduce a population-based model of the transmission dynamics of the liver fluke Opisthorchis viverrini, that allows the mean worm burden in humans to depend on the host age. We parameterise the model using data on intensity of infection in humans and prevalence data for cats, dogs, fish and snails from two island communities in Lao People’s Democratic Republic. We evaluate the steady state solution using a fixed point iteration and estimate the basic reproductive number. We optimise the coverage level of MDA in an adapted model of five age groups to compare varying coverages across age groups. Our results suggest that although adults have the strongest contribution to transmission and campaigns should target adults, if such targeting is operationally infeasible, achieving moderate coverage levels in all age groups can still have a substantial impact on reducing worm burden.

Background: \ud Tens of thousands of people die from dog-mediated rabies annually. Deaths can be prevented through post-exposure prophylaxis for people who have been bitten, and the disease eliminated through dog vaccination. Current post-exposure prophylaxis use saves many lives, but availability remains poor in many rabies-endemic countries due to high costs, poor access, and supply.\ud \ud Methods: \ud We developed epidemiological and economic models to investigate the effect of an investment in post-exposure prophylaxis by Gavi, the Vaccine Alliance. We modelled post-exposure prophylaxis use according to the status quo, with improved access using WHO-recommended intradermal vaccination, with and without rabies immunoglobulin, and with and without dog vaccination. We took the health provider perspective, including only direct costs.\ud \ud Findings: \ud We predict more than 1 million deaths will occur in the 67 rabies-endemic countries considered from 2020 to 2035, under the status quo. Current post-exposure prophylaxis use prevents approximately 56 000 deaths annually. Expanded access to, and free provision of, post-exposure prophylaxis would prevent an additional 489 000 deaths between 2020 and 2035. Under this switch to efficient intradermal post-exposure prophylaxis regimens, total projected vaccine needs remain similar (about 73 million vials) yet 17·4 million more people are vaccinated, making this an extremely cost-effective method, with costs of US$635 per death averted and $33 per disability-adjusted life-years averted. Scaling up dog vaccination programmes could eliminate dog-mediated rabies over this time period; improved post-exposure prophylaxis access remains cost-effective under this scenario, especially in combination with patient risk assessments to reduce unnecessary post-exposure prophylaxis use.\ud \ud Interpretation: \ud Investing in post-exposure vaccines would be an extremely cost-effective intervention that could substantially reduce disease burden and catalyse dog vaccination efforts to eliminate dog-mediated rabies.\ud \ud Funding: \ud World Health Organization.

International audience; Background: Tens of thousands of people die from dog-mediated rabies annually. Deaths can be prevented through post-exposure prophylaxis for people who have been bitten, and the disease eliminated through dog vaccination. Current post-exposure prophylaxis use saves many lives, but availability remains poor in many rabies-endemic countries due to high costs, poor access, and supply.Methods: We developed epidemiological and economic models to investigate the effect of an investment in post-exposure prophylaxis by Gavi, the Vaccine Alliance. We modelled post-exposure prophylaxis use according to the status quo, with improved access using WHO-recommended intradermal vaccination, with and without rabies immunoglobulin, and with and without dog vaccination. We took the health provider perspective, including only direct costs.Findings: We predict more than 1 million deaths will occur in the 67 rabies-endemic countries considered from 2020 to 2035, under the status quo. Current post-exposure prophylaxis use prevents approximately 56 000 deaths annually. Expanded access to, and free provision of, post-exposure prophylaxis would prevent an additional 489 000 deaths between 2020 and 2035. Under this switch to efficient intradermal post-exposure prophylaxis regimens, total projected vaccine needs remain similar (about 73 million vials) yet 17·4 million more people are vaccinated, making this an extremely cost-effective method, with costs of US$635 per death averted and $33 per disability-adjusted life-years averted. Scaling up dog vaccination programmes could eliminate dog-mediated rabies over this time period; improved post-exposure prophylaxis access remains cost-effective under this scenario, especially in combination with patient risk assessments to reduce unnecessary post-exposure prophylaxis use.Interpretation: Investing in post-exposure vaccines would be an extremely cost-effective intervention that could substantially reduce disease burden and catalyse dog vaccination efforts to eliminate dog-mediated rabies.Funding: World Health Organization.

Gambiense human African trypanosomiasis (gHAT) is a parasitic, vector-borne neglected tropical disease that has historically affected populations across West and Central Africa and can result in death if untreated. Following from the success of recent intervention programmes against gHAT, the World Health Organization (WHO) has defined a 2030 goal of global elimination of transmission (EOT). The key proposed indicator to measure achievement of the goal is to have zero reported cases. Results of previous mathematical modelling and quantitative analyses are brought together to explore both the implications of the proposed indicator and the feasibility of achieving the WHO goal. Whilst the indicator of zero case reporting is clear and measurable, it is an imperfect proxy for EOT and could arise either before or after EOT is achieved. Lagging reporting of infection and imperfect diagnostic specificity could result in case reporting after EOT, whereas the converse could be true due to underreporting, lack of coverage, and cryptic human and animal reservoirs. At the village-scale, the WHO recommendation of continuing active screening until there are three years of zero cases yields a high probability of local EOT, but extrapolating this result to larger spatial scales is complex. Predictive modelling of gHAT has consistently found that EOT by 2030 is unlikely across key endemic regions if current medical-only strategies are not bolstered by improved coverage, reduced time to detection and/or complementary vector control. Unfortunately, projected costs for strategies expected to meet EOT are high in the short term and strategies that are cost-effective in reducing burden are unlikely to result in EOT by 2030. Future modelling work should aim to provide predictions while taking into account uncertainties in stochastic dynamics and infection reservoirs, as well as assessment of multiple spatial scales, reactive strategies, and measurable proxies of EOT.

We perform sensitivity analyses on a mathematical model of malaria transmission to determine the relative importance of model parameters to disease transmission and prevalence. We compile two sets of baseline parameter values: one for areas of high transmission and one for low transmission. We compute sensitivity indices of the reproductive number (which measures initial disease transmission) and the endemic equilibrium point (which measures disease prevalence) to the parameters at the baseline values. We find that in areas of low transmission, the reproductive number and the equilibrium proportion of infectious humans are most sensitive to the mosquito biting rate. In areas of high transmission, the reproductive number is again most sensitive to the mosquito biting rate, but the equilibrium proportion of infectious humans is most sensitive to the human recovery rate. This suggests strategies that target the mosquito biting rate (such as the use of insecticide-treated bed nets and indoor residual spraying) and those that target the human recovery rate (such as the prompt diagnosis and treatment of infectious individuals) can be successful in controlling malaria

Background\ud \ud Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment.\ud \ud Methods\ud \ud Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings.\ud \ud Results\ud \ud Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings.\ud \ud Conclusions\ud \ud There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs.

Trypanosoma brucei gambiense causes human African trypanosomiasis (HAT). Between 1990 and 2015, almost 440 000 cases were reported. Large-scale screening of populations at risk, drug donations, and efforts by national and international stakeholders have brought the epidemic under control with, Highlights gambiense-HAT is targeted for elimination with zero transmission in humans. Innovative tools may contribute to the achievement of elimination; these tools include rapid diagnostic tests, improved tsetse-control tools, and an oral drug to treat both stages of disease. Research is revealing associations between infection outcome, including self-cure, and mutations within genes involved in immune responses. Patient-derived T. b. gambiense strains can cycle in animals and tsetse flies without losing infectivity to humans. Molecular and serological techniques facilitate new studies on naturally infected animals as putative reservoir hosts. Mathematical modelling supports the hypothesis that human or animal reservoirs drive transmission, and they, or the tsetse vectors, could be targeted to swiftly impact transmission. Ongoing modelling will assess possible recrudescence via reservoirs.

Highlights • Malaria and many other diseases are currently targeted for elimination. • Prioritisation of areas for elimination often occurs in an ad hoc manner. • In low transmission areas, prioritising higher transmission site reduces total burden. • In low transmission areas, prioritising higher transmission site reduces total costs. • In high transmission areas, prioritisation requires more detailed analysis., Malaria and some other tropical diseases are currently targeted for elimination and eventually eradication. Since resources are limited, prioritisation of countries or areas for elimination is often necessary. However, this prioritisation is frequently conducted in an ad hoc manner. Lower transmission areas are usually targeted for elimination first, but for some areas this necessitates long and potentially expensive surveillance programs while transmission is eliminated from neighbouring higher transmission areas. We use a mathematical model to compare the implications of prioritisation choices in reducing overall burden and costs. We show that when the duration of the elimination program is independent of the transmission potential, burden is always reduced most by targeting high transmission areas first, but to reduce costs the optimal ordering depends on the actual transmission levels. In general, when overall transmission potential is low and the surveillance cost per secondary case compared to the cost per imported case is low, targeting the higher transmission area for elimination first is favoured.

We adapt a population-based model of Opisthorchis viverrini transmission dynamics to determine the effectiveness of three different interventions. The model includes the definitive hosts, humans; the reservoir hosts, dogs and cats; and the intermediate hosts, snails and fish. We consider the interventions: education campaigns to reduce the consumption of raw or undercooked fish, improved sanitation and treatment through mass drug administration. We fit model parameters to a data set from two islands in southern Lao PDR. We calculate the control reproduction number, simulate different scenarios and optimise the interventions with optimal control. We look at the potential of the interventions to eliminate transmission within 20 years. The model shows that education and improved sanitation need a very high coverage to fulfil the goal of elimination, whereas annual drug distribution at medium coverage is sufficient. The best solution is a combination of drug distribution at a medium level of coverage and as high as possible coverage of education and improved sanitation.

Canine rabies transmission was interrupted in N’Djaména, Chad, following two mass vaccination campaigns. However, after nine months cases resurged with re-establishment of endemic rabies transmission to pre-intervention levels. Previous analyses investigated district level spatial heterogeneity of vaccination coverage, and dog density; and importation, identifying the latter as the primary factor for rabies resurgence. Here we assess the impact of individual level heterogeneity on outbreak probability, effectiveness of vaccination campaigns and likely time to resurgence after a campaign. Geo-located contact sensors recorded the location and contacts of 237 domestic dogs in N’Djaména over a period of 3.5 days. The contact network data showed that urban dogs are socially related to larger communities and constrained by the urban architecture. We developed a network generation algorithm that extrapolates this empirical contact network to networks of large dog populations and applied it to simulate rabies transmission in N’Djaména. The model predictions aligned well with the rabies incidence data. Using the model we demonstrated, that major outbreaks are prevented when at least 70% of dogs are vaccinated. The probability of a minor outbreak also decreased with increasing vaccination coverage, but reached zero only when coverage was near total. Our results suggest that endemic rabies in N’Djaména may be explained by a series of importations with subsequent minor outbreaks. We show that highly connected dogs hold a critical role in transmission and that targeted vaccination of such dogs would lead to more efficient vaccination campaigns., Author summary Rabies transmission between dogs and from dogs to humans can be interrupted by mass vaccination of dogs. Novel geo-referenced contact sensors tracked the contacts and locations of several hundred dogs in N’Djaména, the capital of Chad. With the data generated by the sensors we developed a contact network model for rabies transmission dynamics. The model results compared well to incidence data. The model explains the relationship between vaccination campaigns and number of cases better than previous models. Highly connected dogs play a critical role in rabies transmission and targeted vaccination of these dogs would lead to more efficient vaccination campaigns.

OBJECTIVES For tuberculosis (TB) transmission to occur, an uninfected individual must inhale the previously infected breath. Our objective was to identify potential TB transmission hotspots in metropolitan city of Dar es Salaam, Tanzania and to model the annual risk of TB transmission in different locations of public importance. METHODS We collected indoor carbon dioxide (CO2) data from markets, prisons, night clubs, public transportation, religious and social halls, and from schools. Study volunteers recorded social contacts at each of the locations. We then estimated the annual risks of TB transmission using a modified Wells-Riley equation for different locations. RESULTS The annual risks of TB transmission were highest among prison inmates (41.6%) and drivers (20.3%) in public transport. Lower transmission risks were found in central markets (4.8% for traders, but 0.5% for their customers), passengers on public transport (2.4%), public schools (4.0%), nightclubs (1.7%), religious (0.13%), and social halls (0.12%). CONCLUSION For the first time in a country representative of sub-Saharan Africa, we modelled the risk of TB transmission in important public locations by using a novel approach of studying airborne transmission. This approach can guide identification of TB transmission hotspots and targeted interventions to reach WHO's ambitious End TB targets.

Background\ud \ud The ability of mosquitoes to evade fatal exposure to insecticidal nets and sprays represents the primary obstacle to eliminating malaria. However, it remains unclear which behaviours are most important for buffering mosquito and parasite populations against vector control.\ud \ud Methods\ud \ud Simulated life histories were used to compare the impact of alternative feeding behaviour strategies upon overall lifetime feeding success, and upon temporal distributions of successful feeds and biting rates experienced by unprotected humans, in the presence and absence of insecticidal nets. Strictly nocturnal preferred feeding times were contrasted with 1) a wider preference window extending to dawn and dusk, and 2) crepuscular preferences wherein foraging is suppressed when humans sleep and can use nets but is maximal immediately before and after. Simulations with diversion and mortality parameters typical of endophagic, endophilic African vectors, such as Anopheles gambiae and Anopheles funestus, were compared with those for endophagic but exophilic species, such as Anopheles arabiensis, that also enter houses but leave earlier before lethal exposure to insecticide-treated surfaces occurs.\ud \ud Results\ud \ud Insecticidal nets were predicted to redistribute successful feeding events to dawn and dusk where these were included in the profile of innately preferred feeding times. However, predicted distributions of biting unprotected humans were unaffected because extended host-seeking activity was redistributed to innately preferred feeding times. Recently observed alterations of biting activity distributions therefore reflect processes not captured in this model, such as evolutionary selection of heritably modified feeding time preferences or phenotypically plastic expression of feeding time preference caused by associative learning. Surprisingly, endophagy combined with exophily, among mosquitoes that enter houses but then feed and/or rest briefly before rapidly exiting, consistently attenuated predicted insecticide impact more than any feeding time preference trait.\ud \ud Conclusions\ud \ud Regardless of underlying cause, recent redistributions of host-biting activity to dawn and dusk necessitate new outdoor control strategies. However, persistently indoor-feeding vectors, that evade intradomiciliary insecticide exposure, are at least equally important. Fortunately, recent evaluations of occupied houses or odour-baited stations, with baffled entrances that retain An. arabiensis within insecticide-treated structures, illustrate how endophagic but exophilic vectors may be more effectively tackled using existing insecticides.

Malaria and human African trypanosomiasis are two vector-borne diseases caused by protozoa. In Zanzibar, Tanzania, malaria persists at a low prevalence despite the implementation of vector control, passive surveillance, and reactive surveillance. Human movement, and subsequent case importation, is hypothesised to be a key driver of persistence. Human African trypanosomiasis prevalence is below 1000 globally and is targeted for elimination. However, treatment options were previously limited and the diagnosis process is invasive and painful. The introduction of a new oral treatment improves options for treatment but may have an impact on transmission, as compliance levels may be lower than with previous treatments. Stochastic metapopulation models of disease transmission were used to explore a range of questions regarding malaria and human African trypanosomiasis transmission and elimination. A metapopulation model of malaria transmission was developed and parameterised to data from Zanzibar, Tanzania. It incorporated human movement and reactive case detection, and was used to investigate the impact of improvements to reactive case detection or treatment of imported cases on prevalence levels. The model was then expanded to include separate categories for imported, introduced, and indigenous cases, which allowed us to apply the WHO definition of malaria elimination (three years with no indigenous cases). An already established model of human African trypanosomiasis transmission was adapted to incorporate treatment by fexinidazole and potential non-compliance. This was used to test the potential impact of widespread versus limited access to fexinidazole under a range of compliance scenarios, and the potential impact of increased treatment seeking rates. The controlled reproduction number for malaria was estimated to be below the threshold value of 1 on both major islands of Zanzibar, confirming that importation is driving disease persistence. Reactive case detection is estimated to reduce malaria incidence by approximately 10% on Zanzibar. To achieve non-zero probabilities of elimination, infections in travellers need to be targeted, and onward transmission from imported cases needs to be reduced. Considering human African trypanosomiasis transmission, an increase of 20% in the passive detection rate is expected to counter a small negative impact of non-compliance to fexinidazole. While reactive case detection is useful for surveillance and does reduce malaria incidence, the large number of low parasite density infections prevents reactive case detection from removing large parts of the parasite reservoir. The controlled reproduction number needs to be kept well below 1 in order to minimise the chances of any imported cases leading to chains of transmission that lead to indigenous cases. A better understanding of treatment compliance with fexinidazole and changes in treatment seeking behaviour is necessary to better estimate the potential impact of fexinidazole on human African trypanosomiasis transmission in the Democratic Republic of the Congo.

The trematode liver fluke, Opisthorchis viverrini, is endemic in Thailand, Lao People's Democratic Republic (Lao PDR) and Cambodia. Its life cycle involves humans, dogs and cats as definitive hosts; and snails and fish as intermediate hosts. Humans get infected through the consumption of raw or undercooked fish. A severe infection of O. viverrini can lead to cholangiocarcinoma, a mostly fatal bile duct cancer. Control activities include treatment of humans and domestic pets, health education on food consumption and improved sanitation. Mathematical modelling can help us to understand this multi-host disease system, identify weak points in the transmission cycle and determine the effectiveness of combinations of interventions to provide rational advice for the planning of control activities. Analysis and simulation of a series of mathematical models, ranging from deterministic ordinary differential equations models to stochastic individual-based models, calibrated to data from two islands in the Mekong river in Lao PDR, suggest that (i) mass drug administration is necessary for elimination of O. viverrini to be achieved as quickly as possible; (ii) sustainable education campaigns are as important as mass drug administration; and (iii) it is unlikely that cats and dogs are necessary for transmission to persist.

Background: Tuberculosis (TB) is the leading cause of death in the world from a single infectious disease and resulted in about 1.5 million deaths in 2018. Globally, close to one third of the population is latently infected with Mycobacterium tuberculosis (Mtb), of which about 5-10% during their lifetime, will develop active TB depending on the age of infection. TB is an airborne disease transmitted by airways from one person to the next when an uninfected individual breathes in air containing Mtb expired from an infected person. One way to estimate the risk of TB transmission begins with measuring environmental levels of carbon dioxide (CO2) levels exhaled by humans. CO2 levels combined with social contact data allow calculation of the volumes of rebreathed air in order to estimate the potential for airborne disease transmission by considering time at risk, quanta of contagion and the number of people occupying the confined space etc. Unfortunately, most TB patients are diagnosed at later stages of the disease, due to poor health-seeking behavior, inappropriate diagnostic investigations requested by health care providers, and limited access to better TB diagnostics which forces patients to seek relief by using self-prescribed medication. Delaying diagnosis and treatment of TB has important consequences for disease control at both the individual (poor treatment outcome) as well as the community level (continued transmission). Within the country, the prevalence of TB varies considerably across regions, and is higher among males, older persons, and those with lower socioeconomic status. Lastly, patients with TB often have additional comorbidities such as anemia, helminthiasis etc., which can result in poor treatment outcomes. Anemia of chronic disease is primarily found in patients with chronic disease status such as those with chronic immune activation such as TB and HIV-positive patients. Objectives: The overall goal of this PhD project was to understand the epidemiology and transmission of tuberculosis in Tanzania by studying the infrastructure-related risk of TB transmission through measuring environmental CO2 levels at locations of public importance; determining the TB diagnostic delay and its associated factors among TB patients; understanding differences in the epidemiology of TB and comorbidities among TB patients from rural and urban Tanzania; and investigating the association of hepcidin levels with coinfections, TB disease severity and progression from TB infection to disease among adults in Tanzania. Methods: This PhD project was embedded in the ongoing hospital-based cohort of adult TB cases and controls in Temeke, Dar es Salaam and Ifakara, Morogoro, Tanzania. The field work for this PhD study was carried out between September 2016 and April 2018. The project had two designs; infrastructure-related and patient-related design. For objective 1, an observational study was carried out which employed exposure assessment methods where we collected environmental data (CO2, geo-coordinates etc.,) from locations of public importance. We used the modified Wells-Riley equation to estimate the annual risk of TB transmission which was calculated as a function of time spent per year at a given location. For objectives 2-3, we analysed data from the ongoing cohort of adult TB patients and their household contacts (TB DAR). Briefly, recruitment of study participants began in 2013 at Temeke Regional Referral Hospital (Temeke district) and 2014 at the St. Francis Referral Hospital (Kilombero district). Participants collected baseline information and provided specimen for further analysis. Multivariate logistic regression models were used to find associations and presented as crude and adjusted odds ratio. Lastly, for objective 4, we designed a nested case-control study matched by age and sex. Descriptive statistics were used to summarize participants characteristics. We compared cases and controls using conditional logistic regression model to determine associations between outcomes of interest and various predictors. Results: We found that the annual risks of TB transmission were highest among prison inmates (41.6%) and drivers (20.3%) in public transport. Lower transmission risks were found in central markets (4.8% for traders, but 0.5% for their customers), passengers on public transport (2.4%), public schools (4.0%), nightclubs (1.7%), religious (0.13%), and social halls (0.12%). Diagnostic delay was positively associated with absence of chest pain (aOR = 7.97, 95% confidence intervals [CI] = 3.15 – 20.19), and presence of hemoptysis (aOR = 25.37, 95% CI = 11.15 – 57.74) and negatively associated with use of medication prior to TB diagnosis (aOR = 0.31, 95% CI = 0.14 – 0.71). Patients living far from pharmacies were less likely to visit a health care facility (incremental increase of distance versus visit to any facility: OR = 0.51, 95% CI = 0.28 – 0.96). Patients from the rural setting were older (median age 37 years vs. 34 years, p=0.003), had a lower median body mass index (17.5 kg/m2 vs. 18.5 kg/m2, p

Rabies is a viral disease that is transmitted by bite and is fatal after the onset of symptoms. All warm blooded animals are susceptible to rabies and a wide range of species including foxes, wolves, jackals, raccoons, mongooses and bats act as reservoir hosts. Approximately 60,000 people die of rabies every year, mainly in Africa and Asia. The main source of human rabies is the domestic dog. Rabies in humans is preventable by timely administration of post-exposure prophylaxis, with a reduced schedule of administration if the person was protected by pre-exposure prophylaxis. Mass vaccination of dogs is considered effective in preventing human exposure and oral vaccine baits were used to eliminate rabies from foxes in central and western Europe. In N’Djamena, the capital of Chad, rabies is endemic with approximately one confirmed case of dog rabies per week. Each dog exposes on average two humans. In 2012 and 2013 two mass vaccination campaigns of dogs were conducted, reaching a coverage of more than 70% in both years. The campaigns interrupted transmission for nine months, but a resurgence of cases led to re-establishment of rabies at the pre-intervention endemic state. To better understand the movement and contact behaviour of dogs, 300 geo-located contact sensors were deployed on dogs in three different quarters of N’Djamena in 2016. We developed three mathematical models of rabies transmission, calibrated to the incidence data and coverage levels from the campaigns and data on dog movement and contacts from the geo-located contact sensors. We used an ordinary differential equation model to assess the effect of the vaccination campaigns and found that after the campaigns, the effective reproductive ratio dropped below one. Implementing a stochastic version of the model with the Gillespie algorithm confirmed the interruption of transmission. We found that population turnover contributed more to the decrease of vaccination coverage after the campaigns than individual immunity loss. Possible reasons for the resurgence of cases after the campaigns include spatial heterogeneity of vaccination coverage and dog density, underreporting and importation of latent dogs from the surroundings of N’Djamena. We developed a deterministic metapopulation model with importation of latent dogs to investigate the potential reasons for the resurgence seen in 2014. Our results indicate that importation of latently infected dogs better explains the incidence data than heterogeneity or underreporting. Because importation seems to be the most likely reason for the resurgence in cases, we investigated the chains of transmission triggered by imported cases. In order to realistically reproduce the contact heterogeneity at individual level, we used data from 300 geo-located contact sensors to build a network of 5000 dogs. Since there is no established method for expanding a network to a network with more nodes, we have developed and validated a network construction algorithm. We developed an individual based model and calibrated the transmission rate such that the simulation results correspond to outbreak data from two quarters in N’Djamena. We have shown that 70% coverage prevents major but not minor outbreaks. Since highly connected dogs hold a critical role in rabies transmission, vaccinating such dogs could increase the effect of vaccination strategies. Vaccinating dogs is an effective and equitable way of reducing human exposure and should therefore be an inherent of part rabies control programmes in endemic settings. However, in the absence of dog population management, population turnover quickly reduces vaccination coverage and reintroduction from surrounding areas or spillovers from wildlife reservoirs threaten the gains of mass dog vaccination campaigns. This suggests that maintaining high vaccination coverage by either repeated mass vaccination campaigns or continuous vaccination of dogs as well as oral vaccination of reservoirs (which was not investigated here) might be part of the best intervention package for settings like N’Djamena.

Planning for the control of Plasmodium falciparum malaria at the population level demands models of malaria epidemiology that provide realistic quantitative prediction of likely epidemiological outcomes of a wide range of control strategies. This project applies mathematical modeling parameterized both generally and with site-specific field data to better understand transmission dynamics of malaria across sites with varying transmission intensity and seasonality, primarily the highlands of western Kenya and in the lowlands of Zambia's Southern Province. Simulation results explore possible epidemiological scenarios for malaria in the presence and absence of a mix of control interventions, and for different amounts and patterns of seasonality of transmission. Together with a cost effectiveness analysis, results form the basis of recommendations for control programs. Individual-based stochastic models of malaria epidemiology were developed by the Swiss Tropical and Public Health Institute (Swiss TPH). To provide the site-specific parameters needed to fit the models to the study areas data on existing entomological, demographic, intervention deployment and health systems was gathered from field studies conducted by collaborating institutes and a literature review. Model simulations were run on an ensemble of models with multiple random seeds on the OpenMalaria simulator. Simulation outputs were compared to the observed data from the study areas in order to assess the validity of the model and a sensitivity analysis was conducted to address uncertainty. The model was then used to predict the impact of different combinations of malaria control interventions, and the impact of different seasonal transmission patterns, on impact measures. The models were able to simulate the transmission patterns of malaria in the study areas of western Kenyan highlands and Zambia lowlands and gain insight into the potential impact of malaria control interventions currently being un- or under- utilized in these areas. Despite the ability of mathematical modeling to be used to translate between measures of malaria transmission and indicators of disease burden in areas where sparse data renders evidence-based programmatic decision-making challenging, these models remain largely inaccessible to program managers. Results from such models can provide public health officials with accurate estimates of transmission, by seasonal pattern, that are necessary for assessing and tailoring malaria control and elimination programs to specific settings.

In malaria endemic regions, dispersal of mosquitoes from one location to another searching for resources for their survival and reproduction is a fundamental biological process that operates at multiple temporal and spatial scales. This dispersal behaviour is an important factor that causes uneven distribution of malaria vectors causing heterogeneous transmission. Although mosquito dependence in a heterogeneous environment has several implications for malaria vector control and in public health in general, its inclusion in mathematical models of malaria transmission and control has received limited attention. Most models of malaria transmission and control explain relationships between the number of mosquitoes and malaria transmission in humans while assuming enclosed systems of mosquitoes in which spatial dynamics and movements are not taken into account. These models have limited ability to assess and quantify the distribution of risks and interventions at local scales. Therefore, in order to overcome this limitation, mathematical models that consider the interaction between dispersal behaviour, population dynamics, environmental heterogeneity, and age structures of the mosquito are needed for designing, planning, and management of the control strategies at local scales. Advances in malaria modelling have recently begun to incorporate spatial heterogeneity and highlight the need for more spatial explicit models that include all the vital components of ecological interactions. In response to this need, this thesis develops a spatial mathematical model that captures mosquito dispersal and includes all of the above characteristics to achieve a broader and deeper understanding of mosquito foraging behaviour, population dynamics, and its interactions with environmental heterogeneity, distribution of malaria risk, and vector control interventions. The model is applied to assess the impact of dispersal and heterogeneous distribution of mosquito resources on the spatial distribution, dynamics, and persistence of mosquito populations, to estimate the distance travelled by mosquitoes, and to evaluate and assess the impact of spatial distribution of vector control interventions on effectiveness of interventions under mosquitoes' natural dispersal behaviour. Chapter 2 develops a spatial mathematical model of mosquito dispersal in heterogeneous environments with a framework that is simple to allow investigation of aspects that affects malaria transmission. The model incorporates age distribution in form of the aquatic and adult stages of the mosquito life cycle and further divides the adult mosquito population into three stages of the mosquitoes searching for hosts, those resting, and those searching for oviposition sites. These three adult stages provide an opportunity to study the life style of the adult mosquito, and also offer a direct opportunity to assess the impact of interventions targeting different adult states such as insecticide treated bednets (ITNs), indoor residual spraying (IRS), and spatial repellents that reduce contacts between host seeking mosquitoes and human hosts. The spatial characteristics of the model are based on discretization of space into discrete patches. Host and oviposition site searching mosquitoes disperse to the nearest neighbours across the spatial platform where hosts and breeding sites are distributed. In the same Chapter, the model is applied to investigate the effect of heterogeneous distribution of resources used by mosquitoes, estimate the dispersal distance, and to assess the impact of spatial repellents on the dispersal distance. Results revealed that due to dispersal, the distribution of mosquitoes highly depend on the distribution of hosts and breeding sites and the random distribution of spatial repellents reduces the distance travelled by mosquitoes; offering a promising vector control strategy for malaria. In addition, analysis indicated that when only a single patch is considered, and movement ignored, the recruitment parameter and parameters related to the larval and host seeking stages of the mosquito strongly determine mosquito population persistence and extinction. Chapter 3 extends the model developed in Chapter 2 to include vector control interventions. As vector control intervention deployment plans need to consider the spatial distribution of intervention packages, the model extension developed in this chapter is used to examine the effect of spatial arrangement of vector control interventions on their effectiveness. Application of the model to IRS, larvicide, and ITNs showed that randomly distributing these interventions will in general be more effective than clustering them on side of an area. Mosquito dispersal and the different patterns of heterogeneity have different effects on population distribution and dynamics of mosquitoes, and thus, that of malaria. Models that incorporate dispersal when integrated with environmental heterogeneity allow predictions to capture ecological behaviour of mosquitoes, the main source of variations in malaria risk at local spatial scales, providing information needed for determining risk areas for malaria vector control purposes.