Models and analyses to understand threats to polio eradication

A dynamically consistent computational method to solve numerically a mathematical model of polio propagation with spatial diffusion

BACKGROUND AND OBJECTIVE

In this work, a mathematical model based on differential equations is proposed to describe the propagation of polio in a human population. The motivating system is a compartmental nonlinear model which is based on the use of ordinary differential equations and four compartments, namely, susceptible, exposed, infected and vaccinated individuals.

METHODS

In this manuscript, the mathematical model is extended in order to account for spatial diffusion in one dimension. Nonnegative initial conditions are used, and we impose homogeneous Neumann conditions at the boundary. We determine analytically the disease-free and the endemic equilibria of the system along with the basic reproductive number.

RESULTS

We establish thoroughly the nonnegativity and the boundedness of the solutions of this problem, and the stability analysis of the equilibrium solutions is carried out rigorously. In order to confirm the validity of these results, we propose an implicit and linear finite-difference method to approximate the solutions of the continuous model.

CONCLUSIONS

The numerical model is stable in the sense of von Neumann, it yields consistent approximations to the exact solutions of the differential problem, and that it is capable of preserving unconditionally the positivity of the approximations. For illustration purposes, we provide some computer simulations that confirm some theoretical results derived in the present manuscript.

Stopping a polio outbreak in the midst of war: Lessons from Syria

BACKGROUND

Outbreaks of circulating vaccine-derived polioviruses (cVDPVs) pose a threat to the eventual eradication of all polioviruses. In 2017, an outbreak of cVDPV type 2 (cVDPV2) occurred in the midst of a war in Syria. We describe vaccination-based risk factors for and the successful response to the outbreak.

METHODS

We performed a descriptive analysis of cVDPV2 cases and key indicators of poliovirus surveillance and vaccination activities during 2016-2018. In the absence of reliable subnational coverage data, we used the caregiver-reported vaccination status of children with non-polio acute flaccid paralysis (AFP) as a proxy for vaccination coverage. We then estimated the relative odds of being unvaccinated against polio, comparing children in areas affected by the outbreak to children in other parts of Syria in order to establish the presence of poliovirus immunity gaps in outbreak affected areas.

FINDINGS

A total of 74 cVDPV2 cases were reported, with paralysis onset ranging from 3 March to 21 September 2017. All but three cases were reported from Deir-ez-Zor governorate and 84% had received < 3 doses of oral poliovirus vaccine (OPV). After adjusting for age and sex, non-polio AFP case-patients aged 6-59 months in outbreak-affected areas had 2.5 (95% CI: 1.1-5.7) increased odds of being unvaccinated with OPV compared with non-polio AFP case-patients in the same age group in other parts of Syria. Three outbreak response rounds of monovalent OPV type 2 (mOPV2) vaccination were conducted, with governorate-level coverage mostly exceeding 80%.

INTERPRETATION

Significant declines in both national and subnational polio vaccination coverage, precipitated by war and a humanitarian crisis, led to a cVDPV2 outbreak in Syria that was successfully contained following three rounds of mOPV2 vaccination.