We formulate a coupled system of renewal equations for the forces of infections in interacting subgroups through a contact network. We use the theory of order-preserving and sub-homogeneous discrete dynamical systems to show the existence and uniqueness of the disease outbreak final sizes in the sub-populations. We illustrate the general theory through a simple SIR model with exponentially and non-exponentially distributed infectious period.

Middle East respiratory syndrome coronavirus (MERS-CoV) is a zoonotic disease transmitted from dromedary camels to people, which can result in outbreaks with human-to-human transmission. Because it is a subclinical infection in camels, epidemiological measures other than prevalence are challenging to assess. This study estimated the force of infection (FOI) of MERS-CoV in camel populations from age-stratified serological data. A cross-sectional study of MERS-CoV was conducted in Kenya from July 2016 to July 2017. Seroprevalence was stratified into four age groups: <1, 1–2, 2–3 and >3 years old. Age-independent and age-dependent linear and quadratic generalised linear models were used to estimate FOI in pastoral and ranching camel herds. Models were compared based on computed AIC values. Among pastoral herds, the age-dependent quadratic FOI was the best fit model, while the age-independent FOI was the best fit for the ranching herd data. FOI provides an indirect estimate of infection risk, which is especially valuable where direct estimates of incidence and other measures of infection are challenging to obtain. The FOIs estimated in this study provide important insight about MERS-CoV dynamics in the reservoir species, and contribute to our understanding of the zoonotic risks of this important public health threat.

Helicobacter pylori (H. pylori) is present in the stomach of half of the world's population. The force of infection describes the rate at which susceptibles acquire infection. In this article, we estimated the age-specific force of infection of H. pylori in Mexico. Data came from a national H. pylori seroepidemiology survey collected in Mexico in 1987–88. We modelled the number of individuals with H. pylori at a given age as a binomial random variable. We assumed that the cumulative risk of infection by a given age follows a modified exponential catalytic model, allowing some fraction of the population to remain uninfected. The cumulative risk of infection was modelled for each state in Mexico and were shrunk towards the overall national cumulative risk curve using Bayesian hierarchical models. The proportion of the population that can be infected (i.e. susceptible population) is 85.9% (95% credible interval (CR) 84.3%–87.5%). The constant rate of infection per year of age among the susceptible population is 0.092 (95% CR 0.084–0.100). The estimated force of infection was highest at birth 0.079 (95% CR 0.071–0.087) decreasing to zero as age increases. This Bayesian hierarchical model allows stable estimation of state-specific force of infection by pooling information between the states, resulting in more realistic estimates.

The timing and origin of Zika virus (ZIKV) introduction in Brazil has been the subject of controversy. Initially, it was assumed that the virus was introduced during the FIFA World Cup in June–July 2014. Then, it was speculated that ZIKV may have been introduced by athletes from French Polynesia (FP) who competed in a canoe race in Rio de Janeiro in August 2014. We attempted to apply mathematical models to determine the most likely time window of ZIKV introduction in Brazil. Given that the timing and origin of ZIKV introduction in Brazil may be a politically sensitive issue, its determination (or the provision of a plausible hypothesis) may help to prevent undeserved blame. We used a simple mathematical model to estimate the force of infection and the corresponding individual probability of being infected with ZIKV in FP. Taking into account the air travel volume from FP to Brazil between October 2013 and March 2014, we estimated the expected number of infected travellers arriving at Brazilian airports during that period. During the period between December 2013 and February 2014, 51 individuals travelled from FP airports to 11 Brazilian cities. Basing on the calculated force of ZIKV infection (the per capita rate of new infections per time unit) and risk of infection (probability of at least one new infection), we estimated that 18 (95% CI 12–22) individuals who arrived in seven of the evaluated cities were infected. When basic ZIKV reproduction numbers greater than one were assumed in the seven evaluated cities, ZIKV could have been introduced in any one of the cities. Based on the force of infection in FP, basic reproduction ZIKV number in selected Brazilian cities, and estimated travel volume, we concluded that ZIKV was most likely introduced and established in Brazil by infected travellers arriving from FP in the period between October 2013 and March 2014, which was prior to the two aforementioned sporting events.

American cutaneous leishmaniasis (ACL) is a complex disease with a rich diversity of animal host species. This diversity imposes a challenge, since understanding ACL transmission requires the adequate identification of reservoir hosts, those species able to be a source of additional infections. In this study we present results from an ACL cross-sectional serological survey of 51 dogs (Canis familiaris), where we used diagnostic tests that measure dog's exposure to Leishmania spp. parasites. We did our research in Panamá, at a village that has undergone significant ecosystem level transformations. We found an ACL seroprevalence of 47% among dogs, and their exposure was positively associated with dog age and abundance of sand fly vectors in the houses of dog owners. Using mathematical models, which were fitted to data on the proportion of positive tests as function of dog age, we estimated a basic reproductive number (R0 ± s.e.) of 1·22 ± 0·09 that indicates the disease is endemically established in the dogs. Nevertheless, this information by itself is insufficient to incriminate dogs as ACL reservoirs, given the inability to find parasites (or their DNA) in seropositive dogs and previously reported failures to experimentally infect vectors feeding on dogs with ACL parasites.

The kernel of modelling transmission dynamics of infectious diseases lies in constructing the force of infection (FOI). Traditionally, it was based on mass-action law. In this paper, we show, based on survey data of Escherichia coli O157 infection on Scottish cattle farms, that the actual form of FOI deviates greatly from mass-action law. Further, control effectiveness deviates qualitatively: the epidemic of mass-action FOI can be controlled with a control effort larger than the so-called herd immunity, while the epidemic inferred from the survey data of E. coli O157 infection was shown to be difficult to control. This indicates that, at least for E. coli O157 infection on cattle farms, it is risky to rely on models of transmission dynamics that were based on mass-action law to design the optimal intervention programme for infectious diseases. This suggests the importance of collecting epidemic data and model selection from data-driven models to infer the most likely model of transmission dynamics.

Understanding age-specific differences in infection rates can be important in predicting the magnitude of and mortality in outbreaks and targeting age groups for vaccination programmes. Standard methods to estimate age-specific rates assume that the age-specific force of infection is constant in time. However, this assumption may easily be violated in the face of a highly variable outbreak history, as recently observed for acute immunizing infections like measles, in strongly seasonal settings. Here we investigate the biases that result from ignoring such fluctuations in incidence and present a correction based on the epidemic history. We apply the method to data from a measles outbreak in Niamey, Niger and show that, despite a bimodal age distribution of cases, the estimated age-specific force of infection is unimodal and concentrated in young children (<5 years) consistent with previous analyses of age-specific rates in the region.

The paper describes a mathematical model for canine leishmaniasis and presents formulae which can be used to estimate the basic reproduction number, R0. The primary concern has been to devise methods of estimation which make best use of those data most easily obtained by fieldwork, e.g. surveys of prevalence in dog (by age) and sandfly populations. A range of formulae are offered which are more or less demanding of data, and which consequently give more or less precise estimates of R0. They include methods for assessing the influence on R0 of heterogeneous biting rates of sandflies on dogs, in which the essence of heterogeneous transmission can be captured merely by measuring relative rather than absolute contact rates.