Appendix 1. Steps Involved in Data Collection Through Mobile Phones

We have developed our data collection criteria based on the CDC’s Flowchart to Identify and Assess 2019 Novel Coronavirus,⁹ and we have added additional variables for the extended utility of our efforts in identifying infected and controlling the spread (see Table 1 in the text).

Appendix 2. Algorithm

Let O ₁, O ₂, O ₃, O ₄, O ₅ be the outputs recorded during the data collection steps 1 through 5 described in the Appendix 1. The 3 outputs within O₂ are given as

$${\bi {O_{\bf 2}} = \left\{ {{O_{{\bf 2}G}},{O_{{\bf 2}A}},{O_{{\bf 2}R}}} \right\},}$$

and 9 pairs of outputs within O₅ are given as

$${\bi {O_{\bf 5}} = \left\{ {\matrix{ {\left( {{O_{{\bf 5}A}},{D_{{\bf 5}A}}} \right),\left( {{O_{{\bf 5}B}},{D_{{\bf 5}B}}} \right),\left( {{O_{{\bf 5}C}},{D_{{\bf 5}C}}} \right),\left( {{O_{{\bf 5}D}},{D_{{\bf 5}D}}} \right),} \cr {\left( {{O_{{\bf 5}E}},{D_{{\bf 5}E}}} \right),\left( {{O_{{\bf 5}F}},{D_{{\bf 5}F}}} \right),\left( {{O_{{\bf 5}G}},{D_{{\bf 5}G}}} \right),\left( {{O_{{\bf 5}H}},{D_{{\bf 5}H}}} \right),} \cr {\left( {{O_{{\bf 5}I}},{D_{{\bf 5}I}}} \right)} \cr } } \right\}},$$

where the pair O_5i, D_5i for i = A, B, …I represents the respondent’s response regarding the presence or absence of i^th sign and symptom (O_5i) and duration of corresponding sign and symptom (D_5i)

(1) If the set of identifiers, I ₁, for

$${\bi {I_{\bf 1}} = \left\{ {{O_{\bf 3}},{O_{{\bf 5}A}},{O_{{\bf 5}B}},{O_{{\bf 5}C}}} \right\}}$$

is equal to one of the elements of the set C ₁, for

$${{\bi{C}}_{\bi{1}}} = \left\{ {\matrix{ {\matrix{ {\left( {{\bf{1}},{\bf{1}},{\bf{1}},{\bf{1}}} \right)} \cr {\left( {{\bf{1}},{\bf{1}},{\bf{1}},{\bf{0}}} \right)} \cr {\left( {{\bf{1}},{\bf{1}},{\bf{0}},{\bf{0}}} \right)} \cr } } \cr {\left( {{\bf{1}},{\bf{0}},{\bf{1}},{\bf{1}}} \right)} \cr {\left( {{\bf{1}},{\bf{0}},{\bf{0}},{\bf{1}}} \right)} \cr {\left( {{\bf{1}},{\bf{0}},{\bf{1}},{\bf{0}}} \right)} \cr {\left( {{\bf{1}},{\bf{1}},{\bf{0}},{\bf{1}}} \right)} \cr } } \right\},$$

for a respondent, then, send HCRC or MHCRC. If I ₁ is not equal to any of the elements of the set C ₁ then proceed to test criteria (3).

(2) If the set of identifiers, I ₂, for

$${\bi {I_{\bf 2}} = \left\{ {{O_{\bf 4}},{O_{{\bf 5}A}},{O_{{\bf 5}B}},{O_{{\bf 5}C}}} \right\}}$$

is equal to one of the elements of the set C ₁, then send HCRC or MHCRC to that respondent, else proceed to the test criteria (4).

(3) If I ₁ is equal to one of the elements of the set C ₂, for

$${{\bi{C}}_{\bi{2}}} = \left\{ {\matrix{ {\matrix{ {\left( {{\bf{0}},{\bf{1}},{\bf{1}},{\bf{1}}} \right)} \cr {\left( {{\bf{0}},{\bf{1}},{\bf{1}},{\bf{0}}} \right)} \cr {\left( {{\bf{0}},{\bf{1}},{\bf{0}},{\bf{0}}} \right)} \cr } } \cr {\left( {{\bf{0}},{\bf{0}},{\bf{1}},{\bf{1}}} \right)} \cr {\left( {{\bf{0}},{\bf{0}},{\bf{0}},{\bf{1}}} \right)} \cr {\left( {{\bf{0}},{\bf{0}},{\bf{1}},{\bf{0}}} \right)} \cr {\left( {{\bf{0}},{\bf{1}},{\bf{0}},{\bf{1}}} \right)} \cr } } \right\}$$

then the respondent will be sent an NCRC alert.

(4) If I ₂ is equal to one of the elements of the set C ₂, then the respondent will be sent an NCRC alert.

A comparison of test criteria results of (3) and (4) with their corresponding geographic and sociodemographic details will yield further investigations of signs and symptoms based on whether or not an individual in the survey has traveled to coronavirus-affected areas or has had contact with any person who is known to have COVID-19. Here, we focus only on the identification of cases; further analysis techniques are beyond our scope. However, our approach is flexible enough to capture various other associations within the populations.

Appendix 3. Further Computations on the Data Collected

Suppose n and m are individuals in a region who have responded and not responded, respectively, for a mobile phone–based online survey. Responses are randomly associated and not depended on the sickness due to the virus. The pair

$${\bi \left( {\frac{{n}\over{{n + m}}},\frac{{m}\over{{n + m}}}} \right)}$$

yields the proportions of those who have responded and not responded in that region. Notably, we can compute ${\bi \frac{{m}\over{{n + m}}}}$ because the value m is known to us in that region. Here, n ₁ of n are possible cases identified through our algorithm, and m ₁ of m are possible cases of the virus that were not identified by the algorithm because m individuals never responded to the survey. Because n and m are known to us, one of the following relations will hold:

(A2.1) $${\bi \left\{ {n \gt {\bi m} ,{\bi n} = {\bi m} ,{\bi n} \lt {\bi m}} \right\}}$$

Thus, we will see which of the relations listed in (A2.1) is true. When n>m, one of the following relations will hold:

(A2.2) $${\bi \left\{ {\frac{{{{n_{\bf 1}}}}\over{n}} \gt \frac{{{{\bi m_{\bf 1}}}}\over{\bi m}},\frac{{{{\bi n_{\bf 1}}}}\over{\bi n}} = \frac{{{{\bi m_{\bf 1}}}}\over{\bi m}},\frac{{{{\bi n_{\bf 1}}}}\over{\bi n}} \lt \frac{{{{\bi m_{\bf 1}}}}\over{\bi m}}} \right\}}$$

However, we will never know which of the relations in (A2.1) is true because m ₁ were never identified by the algorithm. For example, suppose 2,000 individuals respond to the survey, and of these, 500 individuals do not respond to the survey and 400 are identified as possible cases by the algorithm. If there are 100 possible cases of virus (which we do not have a mechanism to count) among the 500 who never responded, then the relation

$${\bi \frac{{{{n_{\bf 1}}}}\over{n}} = \frac{{{{m_{\bf 1}}}}\over{m}}}$$

is true. Similarly, other relations of (A2.2) could arise when n>m Using a similar argument, we can verify that when other relations of (A2.1) are true, we are still unsure which of the relations in (A2.1) are true. The 2 × 2 contingency options are provided in Figure 2 (in the text) to visualize the data to be generated using the proposed method.

Theorem: Let there be N individuals in a region. The probability that n ₁ cases identified through the AI framework given that there are n individuals responded to the survey is ${\bi \frac{{{{n_{\bf 1}}N}}\over{{{n^{\bf 2}}}}}.}$

Proof: Let N = n + m, and let

$${\bi U = \left\{ {{u_{\bf 1}},{u_{\bf 2}}, \ldots ,{u_n}} \right\}}$$

be the collection of n individuals who responded,

$${\bi V = \left\{ {{v_{\bf 1}},{v_{\bf 2}}, \ldots ,{v_m}} \right\}}$$

be the collection of m individuals who did not responded. Suppose

$${\bi {U_{\bf 1}} = \left\{ {{u_{{a_{\bf 1}}}},{u_{{a_{\bf 2}}}}, \ldots ,{u_{{a_{{n_{\bf 1}}}}}}} \right\} \subset U}$$

is the collection of respondents who are identified as possible cases. Here U ∪ V can be considered the region shown in (a), U shown in (b) and U ₁ in (c) shown in Figure 1 (in the text).

Suppose we define 2 events E ₁ and U using the sets U, V and U ₁ as follows:

E ₁: n ₁ of n responded cases are identified through the algorithm

E : n of N have responded to the survey.

The conditional probability of the event E ₁ given the event E, say, P(E₁/E) is computed as follows:

$${\bi P({E_{\bf 1}}/E) = {{P({E_{\bf 1}} \cap E)} \over {P(E)}} = {{{{{n_{\bf 1}}} \over n}} \over {{n \over N}}} = {{{n_{\bf 1}}N} \over {{n^{\bf 2}}}}}.$$

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