Projects | Sorif Hossain

Current research

Behavioural change in infectious disease models

PhD research, University of Calgary, 2024 – present. Supervisor: Dr. Rob Deardon

When case counts rise, people distance, wear masks and stay home, and transmission falls. When cases drop, they relax again, and transmission rises. Population-level SIR models can capture this feedback through an alarm function: the transmission rate β is reduced by a factor (1 − a_t), where the alarm a_t between 0 and 1 depends on recent incidence.

My work simulates epidemics under different alarm functions, develops and evaluates statistical methods for fitting these models, and applies them to real-world data, including COVID-19 and influenza. The live figure below runs the same model in your browser.

Stochastic runs

(a) Susceptible, infectious and removed

(b) Effective reproduction number R(t)

(c) Alarm function a(x)

Power alarm kSmaller k gives a faster rise in alarm

Disease and data β (transmission rate)Per day, before any behavioural change Infectious period 1/γMean days infectious Smoothing window m Alarm uses mean incidence over the past m days

Peak infectious: –
Peak day: –
Ever infected: –
R(t) below 1 from day: –
Waves: –
Without alarm, ever infected: –

Figure 1. A live SIR model with behavioural change. Choose an alarm function and move the sliders; all three panels update together. Dashed grey lines show the same outbreak with no behavioural change. Population N = 1,000,000 with five initial infections, run for 300 days. Curves are the expected path of the chain-binomial model; tick “Stochastic runs” to add random realizations.

The model

I^*_t ~ Binomial( S_t, 1 − exp[ −β (1 − a_t) I_t / N ] ), R^*_t ~ Binomial( I_t, 1 − e^−γ )

a_t = f(x_t), where x_t is the mean incidence over the previous m days

Power	f(x) = 1 − (1 − x/N)^1/k
Exponential	f(x) = 1 − e^−δx
Hill	f(x) = δ / (1 + (x₀/x)^ν)
Threshold	f(x) = δ · 1(x > H)

R(t) = S_t Σ_{k ≥ t} [1 − e^−β_k/N] e^{−γ(k − t)}, with β_k = β(1 − a_k)

When x is much smaller than N, the power alarm is almost identical to an exponential alarm with δ = 1/(Nk), so those two tabs can give near-identical curves. Model and alarm forms follow Ward, Deardon and Schmidt (2023), Infectious Disease Modelling 8(4), 947–963 (doi:10.1016/j.idm.2023.08.002); the exponential alarm as in Ward, Deardon and Deeth (2025), Canadian Journal of Statistics 53(1), e11828.