From regional pulse vaccination to global disease eradication: insights from a mathematical model of poliomyelitis

Abstract

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, Re, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase Re and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination.Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of Re when pulse vaccination is present.against polio and measles is mass immunisation, which may be regarded as a pulse vaccination [9]. The complex logistics required for these mass-immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination [43].Pulse vaccination has been investigated in several mathematical models, often in disease models with seasonal transmission. Many diseases show seasonal patterns in circulation; thus inclusion of seasonality may be crucial. Agur et al. (1993) argued for pulse vaccination using a model of seasonal measles transmission, conjecturing that the pulses may antagonise the periodic disease dynamics and achieve control at a reduced cost of vaccination [1]. Shulgin et al. (1998) investigated the local stability of the disease-free periodic solution in a seasonally forced population model with three groups: susceptible (S), infected (I) and recovered (R).They considered pulse vaccination and explicitly found the threshold pulsing period [31]. Recently, Onyango and Müller considered optimal periodic vaccination strategies in the seasonally forced SIR model and found that a well-timed pulse is optimal, but its effectiveness is often close to that of constant-rate vaccination [28].In addition to seasonality, spatial structure has been recognised as an important factor for disease dynamics and control [38]. Heterogeneity in the population movement, along with the patchy distribution of populations, suggests the use of metapopulation models describing disease transmission in patches or spatially structured populations or regions. Mobility can be incorporated and tracked in these models in vari...

Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

“…A similar discussion was carried out in [1,29] but the authors focused on situations in which I (t) < 0 for all t > 0, see also [8]. 4. Statement of the main results.…”

“…Discussion. Theoretical biologists have long studied the multiple implications of vaccination in epidemic models [26,9,17,8,6,23,30,4]. Despite many advances, some fundamental questions remain unsolved.…”

“…Many scientific papers have studied the dynamics of a population subject to pulse vaccination from theoretical and applied perspectives [26,9,17,8,6,23,30,4]. A paradigm with practical implications is the presence of chaotic dynamics in many epidemics [6,23].…”

Optimal vaccination strategies and rational behaviour in seasonal epidemics

“…Typically, the objective is to define an optimal vaccination strategy by minimizing combinations of the vaccination effort/cost and of the effective reproduction number R 0 (i.e., the number of secondary infections generated by a primary case) (Müller and Hadeler, 1996;Castillo-Chavez and Feng, 1998;Laguzet and Turinici, 2015a). This can give rise to particularly interesting problems when we consider non-homogeneous models for which vaccination strategy depends on age (Müller and Hadeler, 1996;Castillo-Chavez and Feng, 1998;Tartof et al, 2013), risk-groups (Scott et al, 2015;Long and Owens, 2011) or when it is time-dependent (Onyango and Müller, 2014;d'Onofrio, 2002;Browne et al, 2015;Houy, 2016). The current work is concerned with timedependent epidemic models with vaccination when both the transmission rate and the vaccination are assumed to be periodic.…”

Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

“…In the literature, considerable work can be found on the mathematical modeling of poliomyelitis [9]- [18]. Some of these works refer to vaccination as polio control mechanism [9] [12] [17] [18], using a standard SEIR model [19].…”